nLab quotient group




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


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.


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

  • The quotient groups of any group by itself is the trivial group: G/G=1G/G = 1.

Last revised on May 26, 2022 at 13:36:04. See the history of this page for a list of all contributions to it.