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Mathematics > Representation Theory
Title: Principal 2-blocks with wreathed defect groups up to splendid Morita equivalence
(Submitted on 20 Oct 2023 (v1), last revised 17 May 2024 (this version, v4))
Abstract: We classify principal $2$-blocks of finite groups $G$ with Sylow $2$-subgroups isomorphic to a wreathed $2$-group $C_{2^n}\wr C_2$ with $n\geq 2$ up to Morita equivalence and up to splendid Morita equivalence. As a consequence, we obtain that Puig's Finiteness Conjecture holds for such blocks. Furthermore, we obtain a classification of such groups modulo $O_{2'}(G)$, which is a pure group theoretical result and of independent interest. Methods previously applied to blocks of tame representation type are used. They are, however, further developed in order to deal with blocks of wild representation type.
Submission history
From: Caroline Lassueur [view email][v1] Fri, 20 Oct 2023 16:12:43 GMT (31kb)
[v2] Wed, 15 Nov 2023 09:43:28 GMT (31kb)
[v3] Tue, 7 May 2024 08:16:04 GMT (32kb)
[v4] Fri, 17 May 2024 12:24:28 GMT (32kb)
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