# Finite-automorph-join-closed subnormal subgroup

From Groupprops

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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

A subgroup of a group is termed **finite-automorph-join-closed subnormal** if a join of finitely many of its automorphic subgroups (i.e., subgroups obtained as its images under automorphisms) is a subnormal subgroup.