About the length of laws for finite groups
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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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