Principal 2-blocks with wreathed defect groups up to splendid Morita equivalence

2023/10/20 by Shigeo Koshitani, Koshitani, Shigeo, Caroline Lassueur +3
Computer Science · Mathematics · #16D90 #20C05 #20C15 #20C20 #20C33 #Advanced Algebra and Geometry #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2310.13621

openalex publication_date 2023/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify principal 2-blocks of finite groups G with Sylow 2-subgroups isomorphic to a wreathed 2-group C_2ⁿ\wr C₂ with n≥ 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.

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