Invariants from Dijkgraaf-Witten TQFT on higher-genus surfaces yield new criteria detecting commutativity, nilpotency, supersolvability, and solvability of finite groups via irreducible character degrees.
Navarro Ortega,Characters and blocks of finite groups, London Mathematical Society Lecture Note Series, 250, Cambridge Univ
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On the invariants of finite groups arising in a topological quantum field theory
Invariants from Dijkgraaf-Witten TQFT on higher-genus surfaces yield new criteria detecting commutativity, nilpotency, supersolvability, and solvability of finite groups via irreducible character degrees.