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arXiv · 1112.4559

Lifting in Frattini Covers and A Characterization of Finite Solvable Groups

Robert Guralnick·Pham Huu Tiep
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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.

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Robert Guralnick, Pham Huu Tiep. 2011-12-20. Lifting in Frattini Covers and A Characterization of Finite Solvable Groups. https://arxiv.org/abs/1112.4559

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