# Abelian-quotient not implies cocentral

From Groupprops

This article gives the statement and possibly, proof, of a non-implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., abelian-quotient subgroup) neednotsatisfy the second subgroup property (i.e., cocentral subgroup)

View a complete list of subgroup property non-implications | View a complete list of subgroup property implications

Get more facts about abelian-quotient subgroup|Get more facts about cocentral subgroup

EXPLORE EXAMPLES YOURSELF: View examples of subgroups satisfying property abelian-quotient subgroup but not cocentral subgroup|View examples of subgroups satisfying property abelian-quotient subgroup and cocentral subgroup

## Statement

It is possible to have a group and a normal subgroup such that is an abelian group, so is an abelian-quotient subgroup, but is not equal to , i.e., is not a cocentral subgroup of .