One of the Lepiotas, the tufted Lepiota, L. cristata, has a powerful smell of radishes.
"Among the Mushrooms" by Ellen M. Dallas and Caroline A. Burgin
It seems to be more in the form of a universal veil resembling the veil of some of the lepiotas.
"Studies of American Fungi. Mushrooms, Edible, Poisonous, etc." by George Francis Atkinson
It differs from the Lepiota in having a volva.
"The Mushroom, Edible and Otherwise" by M. E. Hard
Sometimes it is quite easily detached from the cap socket, as in the Lepiota procerus.
"Student's Hand-book of Mushrooms of America, Edible and Poisonous" by Thomas Taylor