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Class-preserving automorphisms of certain HNN extensions of Baumslag-Solitar groups

Wei Zhou|Goansu Kim
대한수학회 (The Korean Mathematical Society)|2016.07|대한수학회보 (Bulletin of the KMS)|제53권 제4호|pp. 1033-1041

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참고문헌

키워드

HNN extensionsresidually finiteconjugacy separableBaumslag-Solitar groups
주제분류수학

초록

We show that, for any non-zero integers $\la$, $\mu$, $\nu$, $\xi$, class-preserving automorphisms of the group $$G(\la, \mu, \nu, \xi) =\cy{a,b,t: b^{-1} a^{\la} b=a^{\mu}, t^{-1} a^\nu t = b^\xi }$$ are all inner. Hence, by using Grossman's result, the outer automorphism group of $G(\la, \pm\la, \nu, \xi)$ is residually finite.

Abstract

We show that, for any non-zero integers $\la$, $\mu$, $\nu$, $\xi$, class-preserving automorphisms of the group $$G(\la, \mu, \nu, \xi) =\cy{a,b,t: b^{-1} a^{\la} b=a^{\mu}, t^{-1} a^\nu t = b^\xi }$$ are all inner. Hence, by using Grossman's result, the outer automorphism group of $G(\la, \pm\la, \nu, \xi)$ is residually finite.

참고문헌 (30)

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