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, l, li, y, & GONG, L (2016). On the finite $p$-groups with unique cyclic subgroup of given order. Turkish Journal of Mathematics 40 (2): 244-249. https://doi.org/10.3906/mat-1501-70

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