Minimal characteristic subgroup

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This article is about a definition in group theory that is standard among the group theory community (or sub-community that dabbles in such things) but is not very basic or common for people outside.
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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 nontrivial subgroup of a group is termed a minimal characteristic subgroup if it is a characteristic subgroup and does not properly contain any nontrivial characteristic subgroup.

Formalisms

In terms of the minimal operator

This property is obtained by applying the minimal operator to the property: nontrivial characteristic subgroup
View other properties obtained by applying the minimal operator