Centralizer-free subgroup
From Groupprops
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 of a group
is said to be centralizer-free if
is trivial.