English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In the representation theory of finite groups, there is a well-known andimportant conjecture, due to Brou\'e saying that for any prime p, if a p-blockA of a finite group G has an abelian defect group P, then A and its Brauercorresponding block B of the normaliser N_G(P) of P in G are derivedequivalent. We prove in this paper, that Brou\'e's abelian defect groupconjecture, and even Rickard's splendid equivalence conjecture are true for thefaithful 3-block A with an elementary abelian defect group P of order 9 of thedouble cover 2.HS of the Higman-Sims sporadic simple group. It then turns outthat both conjectures hold for all primes p and for all p-blocks of 2.HS.

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