Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1501-70
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
