Cyclical subnormal separation in A-groups

Three main results, concerning A-groups in respect of cyclical subnormal separation as defined in, are presented. It is shown in theorem A that any A-group that is generated by elements of prime order and satisfying the cyclical subnormal separation conditions is metabelian. The two other main results give necessary and sufficient conditions for A-groups, that are split extensions of certain abelian p-groups by a metabelian p'-group, to satisfy the cyclical subnormal separation condition. There is also a result which shows that A-groups with elementary abelian Sylow subgroups are cyclically separated as defined. (author). 7 refs