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http://dx.doi.org/10.4134/BKMS.b150491

CLASS-PRESERVING AUTOMORPHISMS OF CERTAIN HNN EXTENSIONS OF BAUMSLAG-SOLITAR GROUPS  

Kim, Goansu (Department of Mathematics Yeungnam University)
Zhou, Wei (School of Mathematics and Statistics Southwest University)
Publication Information
Bulletin of the Korean Mathematical Society / v.53, no.4, 2016 , pp. 1033-1041 More about this Journal
Abstract
We show that, for any non-zero integers ${\lambda}$, ${\mu}$, ${\nu}$, ${\xi}$, class-preserving automorphisms of the group $$G({\lambda},{\mu},{\nu},{\xi})={\langle}a,b,t:b^{-1}a^{\lambda}b=a^{\mu},t^{-1}a^{\nu}t=b^{\xi}{\rangle}$$ are all inner. Hence, by using Grossman's result, the outer automorphism group of $G({\lambda},{\pm}{\lambda},{\nu},{\xi})$ is residually finite.
Keywords
HNN extensions; residually finite; conjugacy separable; Baumslag-Solitar groups;
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