Finite groups with specific numbers of cyclic subgroups satisfy solvability or supersolvability, with a partial extension of the classification of n-cyclic groups for n at least 13.
Characterizing finite solvable groups through the nilpotency probability
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abstract
Given a finite group $G$, we denote by $\nu(G)$ the probability that two randomly chosen elements of $G$ generate a nilpotent subgroup. We prove that if $\nu(G)>1/12,$ then $G$ is solvable.
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math.GR 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Solvability of Groups via Cyclic Subgroup Count
Finite groups with specific numbers of cyclic subgroups satisfy solvability or supersolvability, with a partial extension of the classification of n-cyclic groups for n at least 13.