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arXiv · 1206.0358

Broué's abelian defect group conjecture holds for the double cover of the Higman-Sims sporadic simple group

Shigeo Koshitani·Jürgen Müller·Felix Noeske
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Abstract

In the representation theory of finite groups, there is a well-known and important conjecture, due to Broué saying that for any prime p, if a p-block A of a finite group G has an abelian defect group P, then A and its Brauer corresponding block B of the normaliser N_G(P) of P in G are derived equivalent. We prove in this paper, that Broué's abelian defect group conjecture, and even Rickard's splendid equivalence conjecture are true for the faithful 3-block A with an elementary abelian defect group P of order 9 of the double cover 2.HS of the Higman-Sims sporadic simple group. It then turns out that both conjectures hold for all primes p and for all p-blocks of 2.HS.

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Shigeo Koshitani, Jürgen Müller, Felix Noeske. 2012-06-02. Broué's abelian defect group conjecture holds for the double cover of the Higman-Sims sporadic simple group. https://arxiv.org/abs/1206.0358

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