Bulletin of the Korean Mathematical Society (대한수학회보)

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

  • Chiew Khiam Tang (Institute of Mathematical Sciences Faculty of Science, University of Malaya) ;
  • Peng Choon Wong (Institute of Mathematical Sciences Faculty of Science, University of Malaya)
  • Received : 2023.07.04
  • Accepted : 2023.12.28
  • Published : 2024.05.31
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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.

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References

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