Centralizer-free subgroup

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]

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This article describes a property that arises as the conjunction of a subgroup property: self-centralizing subgroup with a group property (itself viewed as a subgroup property): centerless group
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Definition

Symbol-free definition

A subgroup of a group is said to be centralizer-free if its centralizer within the whole group is trivial.

Definition with symbols

A subgroup $H$ of a group $G$ is said to be centralizer-free if $C_G(H)$ is trivial.