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WEAK POTENCY AND CYCLIC SUBGROUP SEPARABILITY OF CERTAIN FREE PRODUCTS AND TREE PRODUCTS

Kok Bin Wong|Peng Choon Wong|Muhammad Sufi Mohd Asri|Wan Ainun Mior Othman
대한수학회 (The Korean Mathematical Society)|2023.09|대한수학회보 (Bulletin of the KMS)|제60권 제5호|pp. 1375-1390|DOI 10.4134/BKMS.b220715

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참고문헌

키워드

residually finitetree productsGeneralized free productsweakly potentcyclic subgroup separable
주제분류수학

초록

In this note, we shall show that the generalized free products of subgroup separable groups amalgamating a subgroup which itself is a finite extension of a finitely generated normal subgroup of both the factor groups are weakly potent and cyclic subgroup separable. Then we apply our result to generalized free products of finite extensions of finitely generated torsion-free nilpotent groups. Finally, we shall show that their tree products are cyclic subgroup separable.

Abstract

In this note, we shall show that the generalized free products of subgroup separable groups amalgamating a subgroup which itself is a finite extension of a finitely generated normal subgroup of both the factor groups are weakly potent and cyclic subgroup separable. Then we apply our result to generalized free products of finite extensions of finitely generated torsion-free nilpotent groups. Finally, we shall show that their tree products are cyclic subgroup separable.

참고문헌 (26)

  1. R. B. J. T. Allenby, "The potency of cyclically pinched one-relator groups", Archiv der Mathematik, 36(1), pp.204~210 (1981), Springer Science and Business Media LLC[DOI]
  2. R. B. J. T. Allenby, "On locally extended residually finite groups, in Conference on Group Theory (Univ. Wisconsin-Parkside, Kenosha, Wis., 1972)", Lecture Notes in Math, 319, pp.9~17 (1973), Springer
  3. R.B.J.T Allenby, "The residual finiteness of some one-relator groups with torsion", Journal of Algebra, 71(1), pp.132~140 (1981), Elsevier BV[DOI]
  4. M. S. M. Asri, "Criterion for the weak potency of certain HNN extensions", Mathematica Slovaca, 69(2), pp.381~390 (2019), Walter de Gruyter GmbH[DOI]
  5. M.S.M. Asri, "Fundamental Groups of Graphs of Cyclic Subgroup Separable and Weakly Potent Groups", Algebra Colloquium, 28(01), pp.119~130 (2021), World Scientific Pub Co Pte Lt[DOI]
  6. Gilbert baumslag, "A non-Hopfian group", Bulletin of the American Mathematical Society, 68(3), pp.196~198 (1962), American Mathematical Society (AMS)[DOI]
  7. Gilbert Baumslag, "On the Residual Finiteness of Generalised Free Products of Nilpotent Groups", Transactions of the American Mathematical Society, 106(2), pp.193~ (1963), JSTOR[DOI]
  8. B. D. Evans, "Cyclic amalgamations of residually finite groups", Pacific J. Math, 55, pp.371~379 (1974)[DOI]
  9. Rita Gitik, "Graphs and Separability Properties of Groups", Journal of Algebra, 188(1), pp.125~143 (1997), Elsevier BV[DOI]
  10. Emily Hamilton, "Abelian subgroup separability of Haken 3-manifolds and closed hyperbolic n-orbifolds", Proceedings of the London Mathematical Society, 83(3), pp.626~646 (2001), Wiley
  11. A. Karrass, "On the Free Product of Two Groups with an Amalgamated Subgroup of Finite Index in each Factor", Proceedings of the American Mathematical Society, 26(1), pp.28~ (1970), JSTOR
  12. Goansu Kim, "On polygonal products of finitely generated abelian groups", Bulletin of the Australian Mathematical Society, 45(3), pp.453~462 (1992), Cambridge University Press (CUP)[DOI]
  13. G. Kim, "Cyclic subgroup separability of HNN extensions", Bull. Korean Math. Soc, 30(2), pp.285~293 (1993)
  14. G. Kim, "On the residual finiteness of polygonal products of nilpotent groups", Canad. Math. Bull, 35(3), pp.390~399 (1992)[DOI]
  15. 김관수, "Conjugacy separability of certain generalized free products of nilpotent groups", 대한수학회지, 50(4), pp.813~828 (2013), 대한수학회
  16. H. M. Lim, "Residually finite groups", Master, pp.2012
  17. C. Y. Tang, "Conjugacy Separability of Generalized Free Products of Certain Conjugacy Separable Groups", Canadian Mathematical Bulletin, 38(1), pp.120~127 (1995), Canadian Mathematical Society[DOI]
  18. William P. Thurston, "Three dimensional manifolds, Kleinian groups and hyperbolic geometry", Bulletin of the American Mathematical Society, 6(3), pp.357~382 (1982), American Mathematical Society (AMS)[DOI]
  19. B. A. F. Wehrfritz, "The Residual Finiteness of Some Generalised Free Products", Journal of the London Mathematical Society, s2-24(1), pp.123~126 (1981), Wiley[DOI]
  20. P. C. Wong, "Tree products and polygonal products of weakly potent groups", Algebra Colloq, 5(1), pp.1~12 (1998)
  21. Kok Bin Wong, "Polygonal products of residually finite groups", 대한수학회보, 44(1), pp.61~71 (2007), 대한수학회
  22. Kok Bin Wong, "Cyclic subgroup separability of certain graph products of subgroup separable groups", 대한수학회보, 50(5), pp.1753~1763 (2013), 대한수학회
  23. K. B. Wong, "The Weakly Potency of Certain HNN Extensions of Nilpotent Groups", Algebra Colloquium, 21(04), pp.689~696 (2014), World Scientific Pub Co Pte Ltd[DOI]
  24. Wei Zhou, "Abelian subgroup separability of certain generalized free products of free or finitely generated nilpotent groups", Journal of Pure and Applied Algebra, 221(1), pp.222~228 (2017), Elsevier BV[DOI]
  25. Wei Zhou, "Abelian subgroup separability of certain HNN extensions", International Journal of Algebra and Computation, 28(03), pp.543~552 (2018), World Scientific Pub Co Pte Lt[DOI]
  26. Wei Zhou, "CONJUGACY SEPARABILITY OF GENERALIZED FREE PRODUCTS OF FINITELY GENERATED NILPOTENT GROUPS", 대한수학회보, 47(6), pp.1195~1204 (2010), 대한수학회

관련 논문AI추천

Cyclic subgroup separability of certain graph products of subgroup separable groupsKok Bin Wong, Peng Choon Wong대한수학회 · 대한수학회보2013 · 제50권 제5호Conjugacy separability of certain generalized free products of nilpotent groups김관수, C. Y. Tang대한수학회 · 대한수학회지2013 · 제50권 제4호CONJUGACY SEPARABILITY OF GENERALIZED FREE PRODUCTS OF FINITELY GENERATED NILPOTENT GROUPS김관수, C. Y. Tang, Wei Zhou, Wujie Shi대한수학회 · 대한수학회보2010 · 제47권 제6호On the residual finiteness of fundamental groups of graphs of certain groups김관수대한수학회 · 대한수학회지2004 · 제41권 제5호Residual P-Finiteness of Certain Generalized Free Products of Nilpotent Groups김관수, James McCarron, Youngmi Lee경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2008 · 제48권 제3호Outer automorphism groups of polygonal products of certain conjugacy separable groups김관수, Chi Yu Tang대한수학회 · 대한수학회지2008 · 제45권 제6호

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