| group G is called a Dedekind group if all its subgroups are normal in G. A Dedekind group is either abelian or the direct product of the quaternion group of order 8 with a periodic abelian group without elements of order 4. A nonabelian Dedekind group is a Hamiltonian group. A Dedekind group may be thought of as a group where the subgroup generated by its nonnormal cyclic subgroups is trivial. The topic of this dissertation is the investigation of groups where the subgroup generated by the nonnormal cyclic subgroups is a nontrivial proper subgroup of the group.;For any group G, let ;Generalized Dedekind groups are either abelian or periodic groups of nilpotency class two with a cyclic commutator subgroup of order... |
