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arXiv · 1205.4757

On the 5/8 bound for non-Abelian Groups

John Mangual
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Abstract

If we pick two elements of a non-abelian group at random, the odds this pair commutes is at most 5/8, so there is a "gap" between abelian and non-abelian groups \cite{G}. We prove a "topological" generalization estimating the odds a word presenting the fundamental group of an orientable surface $ $ is satisfied. This resolves a conjecture by Langley, Levitt and Rower.

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John Mangual. 2012-05-21. On the 5/8 bound for non-Abelian Groups. https://arxiv.org/abs/1205.4757

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