Principal 2-blocks with wreathed defect groups up to splendid Morita equivalence
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929372210921472 |
|---|---|
| author | Koshitani, Shigeo Lassueur, Caroline Sambale, Benjamin |
| author_facet | Koshitani, Shigeo Lassueur, Caroline Sambale, Benjamin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_13621 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Principal 2-blocks with wreathed defect groups up to splendid Morita equivalence Koshitani, Shigeo Lassueur, Caroline Sambale, Benjamin Representation Theory Group Theory 20C05, 20C20, 20C15, 20C33, 16D90 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. |
| title | Principal 2-blocks with wreathed defect groups up to splendid Morita equivalence |
| topic | Representation Theory Group Theory 20C05, 20C20, 20C15, 20C33, 16D90 |
| url | https://arxiv.org/abs/2310.13621 |