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arXiv · 2607.13720

Cyclic Probability of a Finite Group

Sayanta Chatterjee·Angsuman Das
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Abstract

The cyclic probability, $\theta(G)$, of a finite group $G$, is defined as the probability that two randomly selected elements of $G$ generate a cyclic subgroup of $G$. In this paper, we study various upper and lower bounds of $\theta(G)$ and show that $\theta(G)$ can be used as a criterion for checking nilpotency and solvability of a finite group. We also compare $\theta(G)$ with other group invariants like commuting probability $cp(G)$ and normalized sum of element orders.

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Sayanta Chatterjee, Angsuman Das. 2026-07-15. Cyclic Probability of a Finite Group. https://arxiv.org/abs/2607.13720

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