Details
| Original language | English |
|---|---|
| Pages (from-to) | 71-78 |
| Number of pages | 8 |
| Journal | Advances in Group Theory and Applications |
| Volume | 12 |
| Publication status | Published - Dec 2021 |
Abstract
The first author recently classified the Morita equivalence classes of 2-blocks of finite groups with elementary abelian defect groups of order 32. In all but three cases he proved that the Morita equivalence class determines the inertial quotient of the block. We finish the remaining cases by utilizing the theory of lower defect groups. As a corollary, we verify Broué’s Abelian Defect Group Conjecture in this situation.
Keywords
- 2-block, Morita equivalence, abelian defect group, Broue's conjecture, Broué’s conjecture
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
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In: Advances in Group Theory and Applications, Vol. 12, 12.2021, p. 71-78.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Broue's Conjecture for 2-Blocks with Elementary Abelian Defect Groups of Order 32
AU - Ardito, Cesare Giulio
AU - Sambale, Benjamin
N1 - Funding Information: * We thank Michael Livesey for a very helpful discussion. The first author is sup-ported by the London Mathematical Society (ECF-1920-03). The second author is supported by the German Research Foundation (SA 2864/1-2 and SA 2864/3-1). Funding Information: The first author is supported by the London Mathematical Society (ECF-1920-03). The second author is supported by the German Research Foundation (SA 2864/1-2 and SA 2864/3-1).
PY - 2021/12
Y1 - 2021/12
N2 - The first author recently classified the Morita equivalence classes of 2-blocks of finite groups with elementary abelian defect groups of order 32. In all but three cases he proved that the Morita equivalence class determines the inertial quotient of the block. We finish the remaining cases by utilizing the theory of lower defect groups. As a corollary, we verify Broué’s Abelian Defect Group Conjecture in this situation.
AB - The first author recently classified the Morita equivalence classes of 2-blocks of finite groups with elementary abelian defect groups of order 32. In all but three cases he proved that the Morita equivalence class determines the inertial quotient of the block. We finish the remaining cases by utilizing the theory of lower defect groups. As a corollary, we verify Broué’s Abelian Defect Group Conjecture in this situation.
KW - 2-block
KW - Morita equivalence
KW - abelian defect group
KW - Broue's conjecture
KW - Broué’s conjecture
UR - http://www.scopus.com/inward/record.url?scp=85128556284&partnerID=8YFLogxK
U2 - 10.32037/agta-2021-012
DO - 10.32037/agta-2021-012
M3 - Article
VL - 12
SP - 71
EP - 78
JO - Advances in Group Theory and Applications
JF - Advances in Group Theory and Applications
SN - 2499-1287
ER -