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Critical groups of group representations

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 the symmetric group.

preprint2016arXivOpen access
Christian Gaetz
math.COmath.RT
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Christian Gaetz

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