The paper proposes a delta-invariant encoding of element orders, class sizes, and character degrees that unifies characterization results for finite simple and related groups.
Characterization of the alternating and symmetric groups by the order and conjugacy class sizes
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abstract
We prove that an arbitrary finite group $G$ having the same order and same set of conjugacy class sizes as an alternating or symmetric group $S$ must be isomorphic to $S$. From this and previously known results it follows that the same holds true for every simple group $S$.
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math.GR 1years
2026 1verdicts
CONDITIONAL 1representative citing papers
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Arithmetic invariants for finite simple and related groups
The paper proposes a delta-invariant encoding of element orders, class sizes, and character degrees that unifies characterization results for finite simple and related groups.