Lifting in Frattini Covers and A Characterization of Finite Solvable Groups

Details Lifting in Frattini Covers and A Characterization of Finite Solvable Groups Lifting in Frattini Covers and A Characterization of Finite Solvable Groups

2011-12-20

arxiv.org/abs/1112.4559v1

Mathematics

Group Theory

Scientific paper

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.

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