English

New Lie products for groups and their automorphisms

Group Theory 2015-01-23 v2

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.

Keywords

Cite

@article{arxiv.1501.04670,
  title  = {New Lie products for groups and their automorphisms},
  author = {James B. Wilson},
  journal= {arXiv preprint arXiv:1501.04670},
  year   = {2015}
}
R2 v1 2026-06-22T08:06:25.118Z