Center is quasiautomorphism-invariant
This article gives the statement, and possibly proof, of the fact that for any group, the subgroup obtained by applying a given subgroup-defining function (i.e., center) always satisfies a particular subgroup property (i.e., quasiautomorphism-invariant subgroup)}
View subgroup property satisfactions for subgroup-defining functions View subgroup property dissatisfactions for subgroup-defining functions
Further information: Center
Let be a group. The center of , denoted , is defined as follows:
In other words, is the set of those elements of that commute with every element of .
Let and be groups. A function is termed a quasihomomorphism of groups if whenever commute, we have .
A function from a group to itself is termed a quasiautomorphism if it is a quasihomomorphism and has a two-sided inverse that is also a quasihomomorphism.
Further information: Quasiautomorphism-invariant subgroup
A subgroup of a group is termed quasiautomorphism-invariant if for every quasiautomorphism of the group, the subgroup gets mapped to within itself.