Blocks with central product defect group 𝐷_{2ⁿ}∗𝐶_{2^{𝑚}}

Sambale, Benjamin

doi:10.1090/S0002-9939-2013-11938-6

Blocks with central product defect group $D_{2^n}\ast C_{2^m}$
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Proc. Amer. Math. Soc. 141 (2013), 4057-4069 Request permission

Abstract:

We determine the numerical invariants of blocks with defect group $D_{2^n}\ast C_{2^m}\cong Q_{2^n}\ast C_{2^m}$ (central product), where $n\ge 3$ and $m\ge 2$. As a consequence, we prove Brauer’s $k(B)$-conjecture, Olsson’s conjecture (and more generally Eaton’s conjecture), Brauer’s height zero conjecture, the Alperin-McKay conjecture, Alperin’s weight conjecture and Robinson’s ordinary weight conjecture for these blocks. Moreover, we show that the gluing problem has a unique solution in this case. This paper continues B. Sambale, Blocks with defect group $D_{2^n}\times C_{2^m}$, J. Pure Appl. Algebra 216 (2012), 119–125.

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