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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The subclass algebra associated with a finite group and subgroup

Author: John Karlof
Journal: Trans. Amer. Math. Soc. 207 (1975), 329-341
MSC: Primary 20C05
MathSciNet review: 0367040
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Abstract: Let $ G$ be a finite group and let $ H$ be a subgroup of $ G$. If $ g \in G$, then the set $ {E_g} = \{ hg{h^{ - 1}}\vert h \in H\} $ is the subclass of $ G$ containing $ g$ and $ {\Sigma _{x \in {E_g}}}x$ is the subclass sum containing $ g$. The algebra over the field of complex numbers generated by these subclass sums is called the subclass algebra (denoted by $ S$) associated with $ G$ and $ H$. The irreducible modules of $ S$ are demonstrated, and results about Schur algebras are used to develop formulas relating the irreducible characters of $ S$ to the irreducible characters of $ G$ and $ H$.

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Article copyright: © Copyright 1975 American Mathematical Society

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