Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A note on invariant transversals for normal subgroups

Gerhard Hiss

Abstract

The existence of invariant transversals for a normal subgroup $H$ in a group $G$ is investigated. This yields counterexamples to a conjecture in case $H$ is abelian and $G$ is finite.

A note on invariant transversals for normal subgroups

Abstract

The existence of invariant transversals for a normal subgroup in a group is investigated. This yields counterexamples to a conjecture in case is abelian and is finite.
Paper Structure (3 sections, 6 theorems, 10 equations)

This paper contains 3 sections, 6 theorems, 10 equations.

Table of Contents

  1. Introduction
  2. Characterizations
  3. Finite groups and $G$-invariant transversals

Key Result

Lemma 2.1

Let $T$ be an $H$-invariant transversal for $G/H$. Then $\langle T \rangle \leq C_G( H )$ and $G = H \langle T \rangle = HC_G(H)$.

Theorems & Definitions (13)

  • Conjecture 1.1
  • Lemma 2.1
  • proof
  • Corollary 2.2
  • proof
  • Proposition 2.3
  • proof
  • Lemma 2.4
  • proof
  • Corollary 2.5
  • ...and 3 more