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Critical groups of group representations. (English) Zbl 1346.05298
Summary: This paper investigates the critical group of a faithful representation of a finite group. It computes the order of the critical group in terms of the character values, and gives some restrictions on its subgroup structure. It also computes the precise structure of the critical group both for the regular representation of any finite group, and for the reflection representation of \(\mathfrak{S}_n\).

MSC:
05E10 Combinatorial aspects of representation theory
15B36 Matrices of integers
20C15 Ordinary representations and characters
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