Critical groups of group representations
Copyright policy )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.
8 pages
- University of Minnesota Crookston United States
- University of Minnesota System United States
- University of Minnesota Morris United States
- Massachusetts Institute of Technology United States
- University of Minnesota United States
Ordinary representations and characters, group representation, Matrices of integers, critical group, Combinatorial aspects of representation theory, FOS: Mathematics, Mathematics - Combinatorics, sandpile group, abelian sandpile model, Combinatorics (math.CO), chip firing, Representation Theory (math.RT), Mathematics - Representation Theory
Ordinary representations and characters, group representation, Matrices of integers, critical group, Combinatorial aspects of representation theory, FOS: Mathematics, Mathematics - Combinatorics, sandpile group, abelian sandpile model, Combinatorics (math.CO), chip firing, Representation Theory (math.RT), Mathematics - Representation Theory
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