Browse > Article
http://dx.doi.org/10.7858/eamj.2018.038

NON-HOPFIAN SQ-UNIVERSAL GROUPS  

Lee, Donghi (Department of Mathematics, Pusan National University)
Publication Information
Abstract
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.
Keywords
non-Hopfian group; small cancellation condition; SQ-universality;
Citations & Related Records
연도 인용수 순위
  • Reference
1 G. Arzhantseva, A. Minasyan and D. Osin, The SQ-universality and residual properties of relatively hyperbolic groups, J. Algebra 315 (2007), 165-177.   DOI
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.   DOI
4 S. M. Gersten and H. Short, Small cancellation theory and automatic groups, Invent. Math. 102 (1990), 305-334.   DOI
5 D. Gruber, Infinitely presented C(6)-groups are SQ-universal, J. London Math. Soc. 92 (2015), 178-201.   DOI
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.   DOI
9 D. Lee and M. Sakuma, A family of two generator non-Hopfian groups, Int. J. Algebra Comput. 27 (2017), 655-675.   DOI
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 A. Yu. Olshanski, The SQ-universality of hyperbolic groups, Sbornik: Mathematics 186 (8) (1995), 1199-1211.   DOI
12 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.
13 R. C. Lyndon and P. E. Schupp, Combinatorial group theory, Springer-Verlag, Berlin, 1977.