# Subgroup-conjugating not implies class-preserving

This article gives the statement and possibly, proof, of a non-implication relation between two automorphism properties. That is, it states that every automorphism satisfying the first automorphism property (i.e., subgroup-conjugating automorphism) neednotsatisfy the second automorphism property (i.e., class-preserving automorphism)

View a complete list of automorphism property non-implications | View a complete list of automorphism property implications

Get more facts about subgroup-conjugating automorphism|Get more facts about class-preserving automorphism

## Contents

## Statement

A subgroup-conjugating automorphism of a group (i.e., an automorphism that sends every subgroup to a conjugate subgroup) need not be class-preserving: it need not send every element to a conjugate element.

## Related facts

### Stronger facts

- Universal power not implies class-preserving
- Universal power not implies IA
- Universal power not implies center-fixing
- Subgroup-conjugating not implies IA
- Subgroup-conjugating not implies center-fixing

### Weaker facts

### Converse

## Facts used

## Proof

The proof follows directly from combining facts (1) and (2).