# P-core-automorphism-invariant subgroup

From Groupprops

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]

## Contents

## Definition

Let be a prime number. Let be a p-group, i.e., a (possibly infinite) group in which every element has order equal to a power of . A subgroup of is termed **-core-automorphism-invariant** if for any normal -subgroup of , is invariant under all automorphisms in that subgroup.

In the finite case, this is equivalent to the following: is invariant under the subgroup , where denotes the -core or Sylow-core, i.e., the unique largest normal -subgroup.

For this property in the context of a finite p-group, refer p-core-automorphism-invariant subgroup of finite p-group.