P-core-automorphism-invariant subgroup

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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]


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

In the finite case, this is equivalent to the following: H is invariant under the subgroup O_p(\operatorname{Aut}(G)), where O_p denotes the p-core or Sylow-core, i.e., the unique largest normal p-subgroup.

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

Relation with other properties

Stronger properties

Weaker properties