Details
| Original language | English |
|---|---|
| Pages (from-to) | 4291-4304 |
| Number of pages | 14 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 143 |
| Issue number | 10 |
| Publication status | Published - 1 Oct 2015 |
Abstract
We prove the Alperin-McKay Conjecture for all p-blocks of finite groups with metacyclic, minimal non-abelian defect groups. These are precisely the metacyclic groups whose derived subgroup have order p. In the special case p = 3, we also verify Alperin’s Weight Conjecture for these defect groups. Moreover, in case p = 5 we do the same for the non-abelian defect groups C25 ⋊ C5n. The proofs do not rely on the classification of the finite simple groups.
Keywords
- Alperin-McKay Conjecture, Metacyclic defect groups
ASJC Scopus subject areas
- Mathematics(all)
- Mathematics(all)
- Applied Mathematics
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In: Proceedings of the American Mathematical Society, Vol. 143, No. 10, 01.10.2015, p. 4291-4304.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The Alperin-Mckay conjecture for metacyclic, minimal non-abelian defect groups
AU - Sambale, Benjamin
N1 - Publisher Copyright: © 2015 American Mathematical Society.
PY - 2015/10/1
Y1 - 2015/10/1
N2 - We prove the Alperin-McKay Conjecture for all p-blocks of finite groups with metacyclic, minimal non-abelian defect groups. These are precisely the metacyclic groups whose derived subgroup have order p. In the special case p = 3, we also verify Alperin’s Weight Conjecture for these defect groups. Moreover, in case p = 5 we do the same for the non-abelian defect groups C25 ⋊ C5n. The proofs do not rely on the classification of the finite simple groups.
AB - We prove the Alperin-McKay Conjecture for all p-blocks of finite groups with metacyclic, minimal non-abelian defect groups. These are precisely the metacyclic groups whose derived subgroup have order p. In the special case p = 3, we also verify Alperin’s Weight Conjecture for these defect groups. Moreover, in case p = 5 we do the same for the non-abelian defect groups C25 ⋊ C5n. The proofs do not rely on the classification of the finite simple groups.
KW - Alperin-McKay Conjecture
KW - Metacyclic defect groups
UR - http://www.scopus.com/inward/record.url?scp=84938241197&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-2015-12637-8
DO - 10.1090/S0002-9939-2015-12637-8
M3 - Article
AN - SCOPUS:84938241197
VL - 143
SP - 4291
EP - 4304
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 10
ER -