Universal deformation rings and generalized quaternion defect groups

Details Universal deformation rings and generalized quaternion defect groups Universal deformation rings and generalized quaternion defect groups

2009-09-05

arxiv.org/abs/0909.1031v2

Adv. Math. 225 (2010), 1499-1522

Mathematics

Group Theory

20 pages, 6 figures. The paper has been updated as follows: The results remain true for more general 2-modular blocks with gen

Scientific paper

10.1016/j.aim.2010.04.004

We determine the universal deformation ring R(G,V) of certain mod 2 representations V of a finite group G which belong to a 2-modular block of G whose defect groups are isomorphic to a generalized quaternion group D. We show that for these V, a question raised by the author and Chinburg concerning the relation of R(G,V) to D has an affirmative answer. We also show that R(G,V) is a complete intersection even though R(G/N,V) need not be for certain normal subgroups N of G which act trivially on V.

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