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- W4300488045 abstract "The bifree double Burnside ring $B^Delta(G,G)$ of a finite group $G$ has a natural anti-involution. We study the group $B^Delta_circ(G,G)$ of orthogonal units in $B^Delta(G,G)$. It is shown that this group is always finite and contains a subgroup isomorphic to $B(G)^timesrtimes Out(G)$, where $B(G)^times$ denotes the unit group of the Burnside ring of $G$ and $Out(G)$ denotes the outer automorphism group of $G$. Moreover it is shown that if $G$ is nilpotent then $B^Delta_circ(G,G)cong B(G)^timesrtimes Out(G)$. The results can be interpreted as positive answers to questions on equivalences of $p$-blocks of group algebras in the case that the block is the group algebra of a $p$-group." @default.
- W4300488045 created "2022-10-03" @default.
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- W4300488045 date "2013-06-11" @default.
- W4300488045 modified "2023-10-18" @default.
- W4300488045 title "Orthogonal units of the bifree double Burnside ring" @default.
- W4300488045 doi "https://doi.org/10.48550/arxiv.1306.2622" @default.
- W4300488045 hasPublicationYear "2013" @default.
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