• 제목/요약/키워드: Baumslag-Solitar groups

검색결과 2건 처리시간 0.143초

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

  • Kim, Goansu;Zhou, Wei
    • 대한수학회보
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    • 제53권4호
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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.

RESIDUAL p-FINITENESS OF CERTAIN HNN EXTENSIONS OF FREE ABELIAN GROUPS OF FINITE RANK

  • Chiew Khiam Tang;Peng Choon Wong
    • 대한수학회보
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    • 제61권3호
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    • pp.785-796
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    • 2024
  • 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.