# Automorph-conjugacy is not finite-join-closed

This article gives the statement, and possibly proof, of a subgroup property (i.e., automorph-conjugate subgroup)notsatisfying a subgroup metaproperty (i.e., finite-join-closed subgroup property).This also implies that it doesnotsatisfy the subgroup metaproperty/metaproperties: Join-closed subgroup property (?), .

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## Contents

## Statement

A join of finitely many automorph-conjugate subgroups need not be automorph-conjugate.

## Facts used

### For the Hall subgroups example

## Proof

### The Hall subgroups example

The proof follows directly from facts (1)-(3).