• Title/Summary/Keyword: outer automorphism groups

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OUTER AUTOMORPHISM GROUPS OF POLYGONAL PRODUCTS OF CERTAIN CONJUGACY SEPARABLE GROUPS

  • Kim, Goan-Su;Tang, Chi Yu
    • Journal of the Korean Mathematical Society
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    • v.45 no.6
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    • pp.1741-1752
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    • 2008
  • Grossman [7] showed that certain cyclically pinched 1-relator groups have residually finite outer automorphism groups. In this paper we prove that tree products of finitely generated free groups amalgamating maximal cyclic subgroups have residually finite outer automorphism groups. We also prove that polygonal products of finitely generated central subgroup separable groups amalgamating trivial intersecting central subgroups have residually finite outer automorphism groups.

OUTER AUTOMORPHISM GROUPS OF CERTAIN POLYGONAL PRODUCTS OF GROUPS

  • Kim, Goan-Su
    • Bulletin of the Korean Mathematical Society
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    • v.45 no.1
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    • pp.45-52
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    • 2008
  • We show that certain polygonal products of any four groups, amalgamating central subgroups with trivial intersections, have Property E. Using this result, we derive that outer automorphism groups of polygonal products of four polycyclic-by-finite groups, amalgamating central subgroups with trivial intersections, are residually finite.

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

  • Kim, Goansu;Zhou, Wei
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.4
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    • pp.1033-1041
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    • 2016
  • 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.