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The powerful class of Sylow subgroups of finite groups

Primoz Moravec

Abstract

The paper explores the effect of powerful class of Sylow $p$-subgroups of a given finite group on control of transfer or fusion. We also find an explicit bound for the $p$-length of a $p$-solvable group in terms of the poweful class of a Sylow $p$-subgroup.

The powerful class of Sylow subgroups of finite groups

Abstract

The paper explores the effect of powerful class of Sylow -subgroups of a given finite group on control of transfer or fusion. We also find an explicit bound for the -length of a -solvable group in terms of the poweful class of a Sylow -subgroup.

Paper Structure

This paper contains 4 sections, 3 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Local control
  4. Powerful class and $p$-length

Theorems & Definitions (12)

  • proof
  • proof
  • proof
  • proof
  • proof
  • proof : Proof of Theorem \ref{['thm:2ndgrun']}
  • proof
  • proof
  • proof
  • proof
  • ...and 2 more