# Action-isomorph-free subgroup

From Groupprops

## Contents |

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

## Definition

### Definition with symbols

A subgroup of a group is termed **action-isomorph-free** in if is a normal subgroup of , and the following condition holds.

Suppose be the homomorphism induced by the action of on by conjugation. Suppose is a normal subgroup of with the homomorphism induced by the action of on by conjugation. Suppose, further, that is an isomorphism with the property that:

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