Details
| Original language | English |
|---|---|
| Pages (from-to) | 263-278 |
| Number of pages | 16 |
| Journal | Manuscripta mathematica |
| Volume | 157 |
| Issue number | 1-2 |
| Publication status | Published - 1 Sept 2018 |
| Externally published | Yes |
Abstract
As a generalization of the modular isomorphism problem we study the behavior of defect groups under Morita equivalence of blocks of finite groups over algebraically closed fields of positive characteristic. We prove that the Morita equivalence class of a block B of defect at most 3 determines the defect groups of B up to isomorphism. Over a valuation ring of characteristic 0 we prove similar results for metacyclic defect groups and 2-blocks of defect 4. In the second part of the paper we investigate the situation for p-solvable groups G. Among other results we show that the group algebra of G itself determines if G has abelian Sylow p-subgroups.
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In: Manuscripta mathematica, Vol. 157, No. 1-2, 01.09.2018, p. 263-278.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the blockwise modular isomorphism problem
AU - Navarro, Gabriel
AU - Sambale, Benjamin
N1 - Funding information: The authors like to thank Bettina Eick, Karin Erdmann, David Green, Burkhard Külshammer, Pierre Landrock and Leo Margolis for answering some questions. We also appreciate valuable comments from Gunter Malle. The first author is partially supported by the Spanish Ministerio de Educación y Ciencia Proyectos MTM2016-76196-P and Prometeo II/Generalitat Valenciana. The second author is supported by the German Research Foundation (project SA 2864/1-1).
PY - 2018/9/1
Y1 - 2018/9/1
N2 - As a generalization of the modular isomorphism problem we study the behavior of defect groups under Morita equivalence of blocks of finite groups over algebraically closed fields of positive characteristic. We prove that the Morita equivalence class of a block B of defect at most 3 determines the defect groups of B up to isomorphism. Over a valuation ring of characteristic 0 we prove similar results for metacyclic defect groups and 2-blocks of defect 4. In the second part of the paper we investigate the situation for p-solvable groups G. Among other results we show that the group algebra of G itself determines if G has abelian Sylow p-subgroups.
AB - As a generalization of the modular isomorphism problem we study the behavior of defect groups under Morita equivalence of blocks of finite groups over algebraically closed fields of positive characteristic. We prove that the Morita equivalence class of a block B of defect at most 3 determines the defect groups of B up to isomorphism. Over a valuation ring of characteristic 0 we prove similar results for metacyclic defect groups and 2-blocks of defect 4. In the second part of the paper we investigate the situation for p-solvable groups G. Among other results we show that the group algebra of G itself determines if G has abelian Sylow p-subgroups.
UR - http://www.scopus.com/inward/record.url?scp=85034238586&partnerID=8YFLogxK
U2 - 10.1007/s00229-017-0990-z
DO - 10.1007/s00229-017-0990-z
M3 - Article
AN - SCOPUS:85034238586
VL - 157
SP - 263
EP - 278
JO - Manuscripta mathematica
JF - Manuscripta mathematica
SN - 0025-2611
IS - 1-2
ER -