Generalizing the Hilton–Mislin genus group
Abstract
For any group H, let H be the set of all isomorphism classes of groups K
such that K H . For a finitely generated group H having finite commu-
Ž .tator subgroup H, H , we define a group structure on H in terms of embed-
dings of K into H, for groups K of which the isomorphism classes belong to
Ž . H . If H is nilpotent, then the group we obtain coincides with the genus group
Ž .GG H defined by Hilton and Mislin. We obtain some new results on Hilton Mislin
genus groups as well as generalizations of known results.