Centralizer-free 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]
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
View a complete list of such conjunctions


BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

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.

Relation with other properties