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arXiv · 1405.1764

Supercharacter Theories and Semidirect Products

Alexander Lang
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Abstract

We describe the supercharacter theories of the semidirect product of H and K, $H\rtimes K$ in terms of the supercharacter theories of the direct product of H and K in the case when both H and K are Abelian groups. To do this we introduce the concept of a homomorphism of supercharacter theories. This provides a classification of the supercharacter theories of the dihedral groups of order 2m when m is odd using the known classification of the supercharacter theories of cyclic groups.

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Alexander Lang. 2014-05-07. Supercharacter Theories and Semidirect Products. https://arxiv.org/abs/1405.1764

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