The subclass algebra associated with a finite group and subgroup
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- by John Karlof PDF
- Trans. Amer. Math. Soc. 207 (1975), 329-341 Request permission
Abstract:
Let $G$ be a finite group and let $H$ be a subgroup of $G$. If $g \in G$, then the set ${E_g} = \{ hg{h^{ - 1}}|h \in H\}$ 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 $H$.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 207 (1975), 329-341
- MSC: Primary 20C05
- DOI: https://doi.org/10.1090/S0002-9947-1975-0367040-2
- MathSciNet review: 0367040