nLab
quotient group

Contents

Idea

A quotient group is a quotient object in the category Grp of groups.

Definition

For GG a group and HGH \hookrightarrow G a normal subgroup, the quotient group G/HG/H is the set of cosets, equipped with a group structure induced from GG.

Examples

  • For ABA \hookrightarrow B a morphism between abelian groups the quotient B/AB/A is equivalently the cokernel of the inclusion.

Revised on September 12, 2012 03:37:52 by Toby Bartels (98.19.47.153)