## A sectional characterization of the Dade group

Let k be a field of characteristic p, let P be a finite p-group, where p is an odd prime, and let D(P) be the Dade group of endo-permutation kP-modules. It is known that D(P) is detected via deflation-restriction by the family of all sections of P which are elementary abelian of rank at most 2. In this paper, we improve this result by characterizing D(P) as the limit (with respect to deflation-restriction maps and conjugation maps) of all groups D(T/S) where T/S runs through all sections of P which are either elementary abelian of rank at most 3 or extraspecial of order p^3 and exponent p.

Published in:
Journal of Group Theory, 11, 2, 155-183
Year:
2008
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