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A Schur ring approach to supercharacters of adjoint groups and related subgroups
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Resumo(s)
Using the correspondence between central Schur rings and supercharacter theories for finite groups, we simplify the construction of the standard supercharacter theory for adjoint groups of finite radical rings. If the radical ring R is of odd characteristic and is endowed with an anti-involution σ, we define a supercharacter theory for the subgroup of the adjoint group R◦ , R◦ σ , consisting of elements fixed by σ. This theory extends the one previously defined in [9], when R is a nilpotent algebra over a finite field.
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Palavras-chave
Anéis de Schur Teoria de Supercaracteres Grupo Adjunto Schur rings Supercharacter Theory Adjoint Group