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arXiv · 1501.04670

New Lie products for groups and their automorphisms

James B. Wilson
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Abstract

We generalize the common notion of descending and ascending central series. The descending approach determines a naturally graded Lie ring and the ascending version determines a graded module for this ring. We also link derivations of these rings to the automorphisms of a group. This uncovers new structure in 4/5 of the approximately 11.8 million groups of size at most 1000 and beyond that point pertains to at least a positive logarithmic proportion of all finite groups.

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James B. Wilson. 2015-01-19. New Lie products for groups and their automorphisms. https://arxiv.org/abs/1501.04670

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