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- Title
The power structure of locally nilpotent $$\varvec{p}$$ -groups.
- Authors
Lv, Heng; Chen, Guiyun; Zhou, Wei
- Abstract
We shall extend the research on power structure of finite p-groups in Mann (J Algebra 42:121-135, 1976) to locally nilpotent p-groups. Firstly, we obtain that a locally nilpotent $$P_i$$ -group G with $$|G:\mho _1(G)|< \infty $$ 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 $$P_i$$ -groups, but all of whose proper infinite subgroups are $$P_i$$ -groups. Finally, we show that locally nilpotent $$P_i$$ -groups with all subgroups subnormal are nilpotent.
- Publication
Archiv der Mathematik, 2017, Vol 108, Issue 2, p123
- ISSN
0003-889X
- Publication type
Article
- DOI
10.1007/s00013-016-1000-5