The power structure of locally nilpotent -groups

摘要

We shall extend the research on power structure of finite p-groups in Mann (J Algebra 42:121-135, 1976) to locally nilpotentp-groups. Firstly, we obtain that a locally nilpotent -group G with is an extension of a divisible abelian group by a finite p-group. Next we get the structure of infinite locally nilpotent p-groups which are not -groups, but all of whose proper infinite subgroups are -groups. Finally, we show that locally nilpotent -groups with all subgroups subnormal are nilpotent.