Residual $p$-finiteness of certain HNN extensions of free abelian groups of finite rank
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Let $p$ be a prime. A group $G$ is said to be residually $p$-finite if for each non-trivial element $x$ of $G$, there exists a normal subgroup $N$ of index a power of $p$ in $G$ such that $x$ is not in $N$. In this note we shall prove that certain HNN extensions of free abelian groups of finite rank are residually $p$-finite. In addition some of these HNN extensions are subgroup separable. Characterisations for certain one-relator groups and similar groups including the Baumslag-Solitar groups to be residually $p$-finite are proved.
Abstract
Let $p$ be a prime. A group $G$ is said to be residually $p$-finite if for each non-trivial element $x$ of $G$, there exists a normal subgroup $N$ of index a power of $p$ in $G$ such that $x$ is not in $N$. In this note we shall prove that certain HNN extensions of free abelian groups of finite rank are residually $p$-finite. In addition some of these HNN extensions are subgroup separable. Characterisations for certain one-relator groups and similar groups including the Baumslag-Solitar groups to be residually $p$-finite are proved.
참고문헌 (25)
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