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About the length of laws for finite groups

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Abstract

We prove new upper bounds of the form O(n/log(n)2−ε) for the length of laws that hold for all groups of size at most n — improving on previous results of Bou-Rabee and Kassabov–Matucci. The methods make use of the classification of finite simple groups. Stronger bounds are proved in case the groups are assumed to be nilpotent or solvable.

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  1. TU Dresden, Institut für Geometrie, 01062, Dresden, Germany

    Andreas Thom

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  1. Andreas Thom
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Correspondence to Andreas Thom.

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Thom, A. About the length of laws for finite groups. Isr. J. Math. 219, 469–478 (2017). https://doi.org/10.1007/s11856-017-1487-x

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  • DOI: https://doi.org/10.1007/s11856-017-1487-x

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