Lifting in Frattini Covers and A Characterization of Finite Solvable Groups
Group Theory
2011-12-21 v1 Algebraic Geometry
Representation Theory
Abstract
We prove a lifting theorem for odd Frattini covers of finite groups. Using this, we characterize solvable groups and more generally p-solvable groups in terms of containing a triple of elements of distinct prime power orders with product 1. This is also related to various questions about Fried's modular tower program and properties of Hurwitz spaces of covers of curves.
Cite
@article{arxiv.1112.4559,
title = {Lifting in Frattini Covers and A Characterization of Finite Solvable Groups},
author = {Robert Guralnick and Pham Huu Tiep},
journal= {arXiv preprint arXiv:1112.4559},
year = {2011}
}