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

authored by

Shigeo Koshitani, Caroline Lassueur, Benjamin Sambale

Abstract

We classify principal -blocks of finite groups with Sylow -subgroups isomorphic to a wreathed -group with 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 , which is a purely 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.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

Chiba University

Type

Article

Journal

Annals of Representation Theory

Volume

1

Pages

439-463

No. of pages

24

ISSN

2704-2081

Publication date

03.10.2024

Publication status

E-pub ahead of print

Peer reviewed

Yes

Electronic version(s)

https://doi.org/10.48550/arXiv.2310.13621 (Access: Open)
https://doi.org/10.5802/art.16 (Access: Open)