On the finite $p$-groups with unique cyclic subgroup of given order

Authors

libo Zhao
yangming li
LU GONG

DOI

10.3906/mat-1501-70

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

First Page

244

Last Page

249

Recommended Citation

Zhao, libo; li, yangming; and GONG, LU (2016) "On the finite $p$-groups with unique cyclic subgroup of given order," Turkish Journal of Mathematics: Vol. 40: No. 2, Article 2. https://doi.org/10.3906/mat-1501-70
Available at: https://journals.tubitak.gov.tr/math/vol40/iss2/2