New Lie products for groups and their automorphisms

2015/01/19 by Wilson, James B.
#20D15 #20D25 #20D30 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1501.04670

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.

Related

• Lower central series and split extensions
• Linking of letters and the lower central series of free groups
• Invariants of Automorphic Lie Algebras
• Applications of Lie ring methods to group theory
• Chief factors of Lie algebras