group

Definitions

  • GROUP OF FRANCISCAN FRIARS
    GROUP OF FRANCISCAN FRIARS
  • WordNet 3.6
    • v group arrange into a group or groups "Can you group these shapes together?"
    • v group form a group or group together
    • n group any number of entities (members) considered as a unit
    • n group a set that is closed, associative, has an identity element and every element has an inverse
    • n group (chemistry) two or more atoms bound together as a single unit and forming part of a molecule
    • ***

Additional illustrations & photos:

A GROUP OF MESAS A GROUP OF MESAS
A GROUP OF PUEBLO INDIANS A GROUP OF PUEBLO INDIANS
Two women and a group of children offer food to a girl Two women and a group of children offer food to a girl
A group of six boys and girls A group of six boys and girls
Cafè group of poilus Cafè group of poilus
Group. Old Greek Group. Old Greek
Public writer. Neapolitan group Public writer. Neapolitan group
"Hot Corn." Neapolitan Group "Hot Corn." Neapolitan Group

Webster's Revised Unabridged Dictionary
  • Interesting fact: In the U.S., the sport that causes the most injuries among the age group of 15-24 is basketball
    • Group A cluster, crowd, or throng; an assemblage, either of persons or things, collected without any regular form or arrangement; as, a group of men or of trees; a group of isles.
    • Group (Mus) A number of eighth, sixteenth, etc., notes joined at the stems; -- sometimes rather indefinitely applied to any ornament made up of a few short notes.
    • Group (Biol) A variously limited assemblage of animals or plants, having some resemblance, or common characteristics in form or structure. The term has different uses, and may be made to include certain species of a genus, or a whole genus, or certain genera, or even several orders.
    • Group An assemblage of objects in a certain order or relation, or having some resemblance or common characteristic; as, groups of strata.
    • v. t Group To form a group of; to arrange or combine in a group or in groups, often with reference to mutual relation and the best effect; to form an assemblage of. "The difficulty lies in drawing and disposing, or, as the painters term it, in grouping such a multitude of different objects."
    • ***
Century Dictionary and Cyclopedia
  • Interesting fact: The music group Simply Red got its name from band member Mick Hucknall, who has red hair
    • n group An assemblage of persons or things; a number of persons or things gathered together with or without regular interconnection or arrangement; a cluster.
    • n group In the fine arts, an assemblage of figures which have some relation to one another and to the general design; a combination of several figures forming a harmonious whole.
    • n group In scientific classifications, a number of individual things or persons related in some definite or classificatory way.
    • n group Specifically— In zoology, any assemblage or classificatory division of animals below the kingdom and above the species: generally said of intermediate or not regularly recognized divisions, or by way of non-committal to the exact taxonomic value of the division thus indicated.
    • n group In geology, a division in the geological sequence or classification of the stratified fossiliferous rocks inferior in value to a system or series. See system.
    • n group In music: A short rapid figure or division, especially when sung to a single syllable.
    • n group A section of an orchestra, comprising the instruments of the same class: as, the wood-wind group.
    • n group In mathematics, a set of substitutions (or other operations) such that every product of operations of the set itself belongs to the set; a system of conjugate substitutions; a set of permutations resulting from performing all the substitutions of a conjugate system upon a series of elements; a set of functions produced by the n operations of a group of operations from n independent functions, called the fundamental system of the group. The order or degree of a group is the number of substitutions it contains; its index is this number divided into the whole number of permutations of the elements of the substitutions.
    • n group A group of infinitely many but discrete operations, among which infinitely small transformations occur.
    • n group in mathematics, a group whose elements have each k indices, or are arranged in a matrix of k dimensions.
    • n group In Capelli's extended sense, groups which can be separated each into the same number of subgroups, so that a substitution of a subgroup in the one can be so coordinated to one of the other that products shall correspond to products.
    • group To form into a group or into groups; arrange in a group or in groups; separate into groups: commonly with reference to the special mutual relation of the things grouped, to classification, or to some special design or purpose, as artistic effect.
    • group To fall into combination or arrangement; form a group or part of a group: used chiefly with reference to artistic effect.
    • group See groop.
    • n group In the recommendations of the International Geological Congress this term is applied, in geological classification, to stratigraphic divisions of the highest order comprising several terrains. Its equivalent term in the time scale is era.
    • n group In combinatorial analysis, one of the classes into which the objects are distributed when the order of the objects in a particular class is material.
    • n group In group-theory, a set of definite operations containing the operation compounded of any two of the set, and also the inverse of every operation of the set.
    • n group In crystallography, a class of crystals characterized by the same degree of symmetry. Each crystalline system embraces several such groups or classes. See symmetry, where the names commonly employed in designating the more important of these groups are given.
    • n group In ethnology, a number of people united together by common habits and usages.
    • ***
Chambers's Twentieth Century Dictionary
  • Interesting fact: In April 1964, The Beatles had the top five songs in the United States. This is the only time that the top five songs at any one time were by the same group.
    • n Group grōōp a number of persons or things together: a number of individual things related, in some definite way differentiating them from others:
    • v.t Group to form into a group or groups
    • v.i Group to fall into harmonious combination
    • n Group grōōp (art) a combination of figures forming a harmonious whole
    • ***

Quotations

  • Joan Rivers
    Joan Rivers
    “My routines come out of total unhappiness. My audiences are my group therapy.”
  • Milton Berle
    Milton Berle
    “Committee--a group of men who keep minutes and waste hours.”
  • Milton Berle
    Milton Berle
    “A committee is a group that keeps minutes and loses hours.”
  • Richard Harkness
    Richard Harkness
    “Committee: A group of the unwilling, picked from the unfit to do the unnecessary.”
  • Friedrich Nietzsche
    Friedrich%20Nietzsche
    “Madness is something rare in individuals -- but in groups, parties, peoples, ages it is the rule.”
  • Stephane Mallarme
    Stephane Mallarme
    “The poetic act consists of suddenly seeing that an idea splits up into a number of equal motifs and of grouping them; they rhyme.”

Etymology

Webster's Revised Unabridged Dictionary
F groupe, It. gruppo, groppo, cluster, bunch, packet, group; of G. origin: cf. G. kropf, craw, crop, tumor, bunch. See Crop (n.)
Chambers's Twentieth Century Dictionary
Fr. groupe—It. groppo, a bunch, knot—Teut.; cf. Ger. kropf, protuberance.

Usage

In literature:

Both mountain groups are dotted with lakes; those of the western group are the largest of the island.
"The Book of the National Parks" by Robert Sterling Yard
Therefore, to increase the efficiency and output of the group will not increase the group labor demand, and group wages.
"The Settlement of Wage Disputes" by Herbert Feis
Almost the whole of a child's knowledge is composed of these groupings.
"A Practical Enquiry into the Philosophy of Education" by James Gall
The selection and grouping of these objects is spoken of as the composition of the picture.
"English: Composition and Literature" by W. F. (William Franklin) Webster
The speeding car, a big one loaded with men, was a hundred yards away and going like the wind before the startled group regained its senses.
"Anderson Crow, Detective" by George Barr McCutcheon
We will consider these minor injuries in groups to remember them more easily.
"Scouting For Girls, Official Handbook of the Girl Scouts" by Girl Scouts
The In-Group and the Out-Group.
"Introduction to the Science of Sociology" by Robert E. Park
The strong and general human tendency to procrastination is shown in the progressive weakening of the various words in this group.
"English Synonyms and Antonyms" by James Champlin Fernald
Menard looked about the group.
"The Road to Frontenac" by Samuel Merwin
This great Artificer worked along four main lines, and hence animals could be divided into four groups.
"The Meaning of Evolution" by Samuel Christian Schmucker
Positives and negatives may not charge at the same rate, and one group may become fully charged before the other group.
"The Automobile Storage Battery" by O. A. Witte
Snap, who was in the group near Grantline at the windows, gasped.
"Astounding Stories of Super-Science, May, 1930" by Various
We finally have to consider the group of suicidal cases.
"Benign Stupors" by August Hoch
Next above the human horde is represented the forced association of men in groups, each group struggling for its own existence.
"History of Human Society" by Frank W. Blackmar
The former was employed in all the other groups, with one exception, the red line group.
"Ancient art of the province of Chiriqui, Colombia" by William Henry Holmes
Little groups were forming at the corners, good-natured groups who seemed to know that they were not to be molested.
"In the Heart of a Fool" by William Allen White
The group on the ground watched, open-mouthed, despite the fact that they themselves were flyers of no mean ability.
"Aces Up" by Covington Clarke
Maybe the twelfth group of numbers has a clue.
"The Caves of Fear" by John Blaine
At the foot of the cliff he found Barkoo and Korgul and Torbat talking with a group of warriors.
"Warrior of the Dawn" by Howard Carleton Browne
The other mass organizations include trade unions, youth groups, athletic societies, and similar interest groups.
"Area Handbook for Bulgaria" by Eugene K. Keefe, Violeta D. Baluyut, William Giloane, Anne K. Long, James M. Moore, and Neda A. Walpole
***

In poetry:

Groups of them met at yet closed portals,
And huddled round the gate,
Patient, as smit by the Immortals,
And helots as by Fate.
"Two Visions" by Alfred Austin
A shepherd group in distance dim
Lie stretched upon the heather,
And with a simple evening hymn
Wake the still breeze together.
"The House In The Heath" by Annette Von Droste-Hulshoff
Believe, on such a group he smiled,
Though he might sigh the while;
Believe not, sweet-souled Mary's child
Was born without a smile.
"The Mother Mary" by George MacDonald
I found no brotherhood in man;
But here and there a vicious clan;
No truth, no love, no justice find
Their way into these groups unkind.
"The Love Amie" by Marcus Mosiah Garvey
Or thronging all one porch of Paradise
A group of Houris bow'd to see
The dying Islamite, with hands and eyes
That said, We wait for thee.
"The Palace of Art" by Alfred Lord Tennyson
Ah! wondrous soon our feast before
A lessening group was yearly spread,
And all our joys were ruffled o'er
With somber mem'ries of the dead.
"Forty Years After" by John Marchborn Cooley

In news:

Freudenberg Nonwovens, a business group within the Freudenberg Group, has announced plans to reorganize its staple fiber business at its headquarters in Weinheim, Germany.
Tracy Della Vecchia is founder of the group, Marine Parents, a national group based in Columbia.
Self-storage operator Big Yellow Group PLC is providing storage space to Little Bundles, a local charity group benefiting families in need, at its Gloucester, England, facility on Eastern Avenue.
Stratus Group buys commercial printer Stratus Group Inc, of Cincinnati, OH, has purchased Budget Printing Inc, located in Orlando, FL.
Chinese e-commerce giant Alibaba Group, which may make a bid for Yahoo, has hired The Duberstein Group.
Gilt Groupe Co-Founder Alexandra W Wilson with Maggie Grace at the GILT GROUPE Celebrity Stylist dinner at Chateau Marmont.
A group of taggers feels Santa Clara County prosecutors have overreacted by labeling their group as a gang.
Scott Walker's plans to serve beer and brats to a bipartisan group of lawmakers has upset the leader of the group that successfully lobbied for Prohibition decades ago.
International Textile Group (ITG) has entered into a joint venture with Hong Kong-based China Ting Group to build a dyeing and finishing plant in the Linping Industrial Area of Hangzhou, China.
K&D Group The K&D group planned to remake the vacant Ameritrust complex into shops, offices, homes and a hotel.
Decked in his most futuristic gold suit of armor, Cee Lo Green took the stage with his group hip-hop group Goodie Mob on Monday's 'The Voice.
The Togolese group cites as its inspiration a strike organized in 2003 by a women's peace group to encourage the end of the Second Liberian Civil War.
A group of grain traders can proceed with a lawsuit to overturn new price-settlement rules at CME Group that they say are killing business in the historic open-outcry trading pits, a judge in Chicago ruled on Monday.
The group of Russian spies that was arrested last year after living undercover in the United States was using technology used by terrorist groups to pass covert information, according to FBI documents released on Monday.
A group of atheists in Florida spent part of their weekend washing away a blessing placed upon a local highway by a religious group.
***

In science:

We consider a special class of so-called hyperbolic groups – the modular group P SL(2, ZZ), and some of its generalizations – the Hecke groups Hq and the braid group B3 .
Random walks on hyperbolic groups and their Riemann surfaces
The Weyl group N/T is cyclic of order two, generated by the class of x (the linear group L2 (q) is a Chevalley group of type A1 and the unitary group U3 (q) is a twisted Chevalley group of type 2A2 ).
Finite simple groups and localization
Note that, with this choice, P On (F ) and P S pn (F ) may not be the group of F rational points of the corresponding algebraic group, because the quotient groups may have F points not in the image of the group of F points of On or S pn .
Generic algebras with involution of degree 8m
The free constructions specified bellow refer to the category of G − groups [F1], consisting of groups together with a group action, and equivariant group homomorphisms.
The nonabelian bar resolution
They are essentially QHSAs on free abelian finite rank n groups A which, with each iteration, first select a random cyclic direct summand Z of the group A and then apply one iteration of the standard Shor algorithm to produce a random character of the “approximating” finite group eA, called a group probe.
Quantum Hidden Subgroup Problems: A Mathematical Perspective
The group corresponding to a subalgebra G of Kil(g ) is called group of motions or group of isometries and denoted by Gr where r, the order of the group, is the number of generators.
On the SO(2,1) symmetry in General Relativity
The general linear group and the symmetric group S (n) are the two most important groups in mathematics and the representation theory of both groups is saturated with partitions.
The uses of random partitions
This is either a cyclic group of prime order or an alternating group of degree n > 5 or a group of Lie type or one of the twenty-six sporadic groups.
Simple Bol loops
Recall (see ) that a group G is said to be residual ly finite if the intersection of all its normal subgroups of finite index is the identity group. A group G is residually finite if and only if, for every element g ∈ G, g 6= 1 there is a homomorphism of G into a finite group that takes g to a nonidentity element.
Simple Bol loops
It is known that: i) any connected algebraic group G has unique normal linear algebraic subgroup H such that the quotient group G/H is an Abelian variety; ii) any linear algebraic group G has a maximum connected solvable normal subgroup (a radical) K such that the quotient group G/K is semisimple.
Simple Bol loops
Known fact for solvable groups: Since, the composition factor of a finite solvable group are cyclic groups, Lemma 2 implies that every solvable group has Ordered Genearating System.
Ordered Generating Systems of Finite Non-Abelian Groups
After defining a linear algebraic group in the first section, we introduce the notions of tori, reductive groups, semisimple groups and the simple algebraic groups.
Arithmetic of algebraic groups
Since a reductive algebraic group admits an almost direct decomposition into simple algebraic groups and a torus, it is necessary to study simple groups and tori to understand the structure of reductive algebraic groups.
Arithmetic of algebraic groups
The aim of this chapter is to investigate the situation for the finite semisimple groups. A finite semisimple group is defined to be the group of Fq -rational points of a simply connected, split, semisimple algebraic group defined over Fq .
Arithmetic of algebraic groups
Since every (simply connected) semisimple algebraic group is a direct product of (simply connected) simple algebraic groups, we get that whenever a finite semisimple group H (Fq ) does not have any of the above groups as direct factors, then the characteristic of Fq contributes the largest to the order of H (Fq ).
Arithmetic of algebraic groups
***