- Turkish Journal of Mathematics
- Vol: 40 Issue: 2
- On the finite $p$-groups with unique cyclic subgroup of given order
On the finite $p$-groups with unique cyclic subgroup of given order
Authors : Libo Zhao, Yangming Li, Lu Gong
Pages : 244-249
View : 5 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :In this paper, we prove that if $G$ is nonabelian and $|G|>p^4$, then $G$ has a unique cyclic subgroup of order $p^m$ with $m\geq 3$ if and only if $G$ has a unique abelian subgroup of order $p^3$ if and only if $G$ is a $2$-group of maximal class.Keywords : $p$-group of maximal class, extra-special $p$-group