Abstrakt: |
Abstract: Let $\alpha$ and $\beta$ be automorphisms of a nilpotent $p$-group $G$ of finite rank. Suppose that $\langle(\alpha\beta(g))(\beta\alpha(g))^{-1} g\in G\rangle$ is a finite cyclic subgroup of $G$, then, exclusively, one of the following statements holds for $G$ and $\Gamma$, where $\Gamma$ is the group generated by $\alpha$ and $\beta$. (i) $G$ is finite, then $\Gamma$ is an extension of a $p$-group by an abelian group. (ii) $G$ is infinite, then $\Gamma$ is soluble and abelian-by-finite. |