J -Groups, L-Groups, and S-Groups

J -Groups, L-Groups, and S-Groups The rtffr group G is called a J -group if G is isomorphic to each subgroup of finite index in G, G is called an L-group if G is locally isomorphic to each subgroup of finite index in G, and G is an S-group if each subgroup of finite index in G is G-generated. Obviously

J -groups ⇒ L-groups ⇒ S-groups. In the first half of the chapter we will discuss how the torsion subgroup of Ext1Z(G,G) is related to (finitely) faithful S-groups. In the second half of the chapter we will scrutinize the converse relationships L-groups ⇒ J -groups, and finitely faithful S-groups ⇒ J -groups.