East Asian mathematical journal

  • 제34권5호
  • /
  • Pages.587-595
  • /
  • 2018
  • /
  • 1226-6973(pISSN)
  • /
  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

NON-HOPFIAN SQ-UNIVERSAL GROUPS

  • Lee, Donghi (Department of Mathematics, Pusan National University)
  • 투고 : 2018.05.16
  • 심사 : 2018.07.03
  • 발행 : 2018.09.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In [9], Lee and Sakuma constructed 2-generator non-Hopfian groups each of which has a specific presentation ${\langle}a,b{\mid}R{\rangle}$ satisfying small cancellation conditions C(4) and T(4). In this paper, we prove the SQ-universality of those non-Hopfian groups.

키워드

참고문헌

  1. G. Arzhantseva, A. Minasyan and D. Osin, The SQ-universality and residual properties of relatively hyperbolic groups, J. Algebra 315 (2007), 165-177. https://doi.org/10.1016/j.jalgebra.2007.04.029
  2. B. Baumslag and S. J. Pride, Groups with two more generators than relators, J. London Math. Soc. 17 (3) (1978), 425-426.
  3. B. Fine and M. Tretkoff, On the SQ-universality of HNN groups, Proc. Amer. Math. Soc. 73 (3) (1979), 283-290. https://doi.org/10.1090/S0002-9939-1979-0518506-2
  4. S. M. Gersten and H. Short, Small cancellation theory and automatic groups, Invent. Math. 102 (1990), 305-334. https://doi.org/10.1007/BF01233430
  5. D. Gruber, Infinitely presented C(6)-groups are SQ-universal, J. London Math. Soc. 92 (2015), 178-201. https://doi.org/10.1112/jlms/jdv022
  6. G. Higman, B. . Neumann and H. Neumann, Embedding theorems for groups, J. London Math. Soc. 24 (1949), 247-254.
  7. J. Howie, On the SQ-universality of T (6)-groups, Forum Math. 1 (3) (1989), 251-272.
  8. D. Lee and M. Sakuma, Epimorphisms between 2-bridge link groups: homotopically trivial simple loops on 2-bridge spheres, Proc. London Math. Soc. 104 (2012), 359-386. https://doi.org/10.1112/plms/pdr036
  9. D. Lee and M. Sakuma, A family of two generator non-Hopfian groups, Int. J. Algebra Comput. 27 (2017), 655-675. https://doi.org/10.1142/S0218196717500321
  10. K. I. Lossov, SQ-universality of free products with amalgamated finite subgroups, Sibirsk. Mat. Zh. 27 (6) (1986), 128-139, 225 (in Russian).
  11. R. C. Lyndon and P. E. Schupp, Combinatorial group theory, Springer-Verlag, Berlin, 1977.
  12. A. Yu. Olshanski, The SQ-universality of hyperbolic groups, Sbornik: Mathematics 186 (8) (1995), 1199-1211. https://doi.org/10.1070/SM1995v186n08ABEH000063
  13. G. S. Sacerdote and P. E. Schupp, SQ-universality in HNN groups and one relator groups, J. London Math. Soc. 7 (2) (1974), 733-740.