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arXiv · 1412.1995

Asypmtotic Behaviour of the Conjugacy Probability of the Alternating Group

Misja F. A. Steinmetz·Madeleine L. Whybrow
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Abstract

For $G$ a finite group, let $κ(G)$ be the probability that $σ,τ\in G$ are conjugate, when $σ$ and $τ$ are chosen independently and uniformly at random. In this paper, we extend the methods of Blackburn et al [2012] to show that $n^2κ(A_n) \to A$ as $n\to\infty$ for a constant $A$, which we will give explicitly.

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Misja F. A. Steinmetz, Madeleine L. Whybrow. 2015-12-22. Asypmtotic Behaviour of the Conjugacy Probability of the Alternating Group. https://arxiv.org/abs/1412.1995

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