Exponent-Critical Groups
Group Theory
2024-04-22 v2
Abstract
We define and investigate the property of being `exponent-critical' for a finite group. A finite group is said to be exponent-critical if its exponent is not the least common multiple of the exponents of its proper non-abelian subgroups. We explore properties of exponent-critical groups and give a characterization of such groups. This characterization generalises a classical result of Miller and Moreno on minimal non-abelian groups; interesting families of -groups appear.
Cite
@article{arxiv.2401.07834,
title = {Exponent-Critical Groups},
author = {Simon R. Blackburn and William Cocke and Andrew Misseldine and Geetha Venkataraman},
journal= {arXiv preprint arXiv:2401.07834},
year = {2024}
}
Comments
18 pages. Minor revisions to introduction and abstract