Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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GENERATING PAIRS FOR THE HELD GROUP He

  • Ashrafi, Ali-Reza (Department of Mathematics, Faculty of Science, University of Kashan)
  • Published : 2002.09.01

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Abstract

A group G is said to be (l, n, n)-generated if it is a quotient group of the triangle group T(p,q,r)=(x,y,z|x$\^$p/=y$\^$q/=z$\^$r/=xyz=1). In [15], the question of finding all triples (l, m, n) such that non-abelian finite simple groups are (l , m, n)-generated was posed. In this paper we partially answer this question for the sporadic group He. We continue the study of (p, q, r) -generations of the sporadic simple groups, where p, q, r are distinct primes. The problem is resolved for the Held group He.

Keywords

References

  1. (p,q,r)-Generation and nX-Complementary Generation of the Sporadic Group Th A. R. Ashrafi
  2. Bull. Austral. Math. Soc. v.30 Some results on quotients of triangle groups M. D. E. Conder
  3. Proc. Amer. Math. Soc. v.116 The symmetric genus of sporadic groups M. D. E. Conder;R. A. Wilson;A. J. Wolder
  4. Atas of Finite Groups J. H. Conway;R. T. Curtis;S. P. Norton;R. A. Parker;R. A. Wilson
  5. Kumomoto J. Math. v.13 (2,p,q)-Generation of the Conway group $Co_1$ M. R. Darafsheh;A. R. Ashrafi
  6. Kumomoto J. Math. v.14 (p,q,r)-Generations of the Conway group $Co_1$, for odd p M. R. Drafsheh;A. R. Ashrafi;G. A. Moghani
  7. to appear in LMS lecture note serries (p,q,r)-Generations of the Sporadic group O'N M. R. Darafsheh;A. R. Ashrafi;G. A. Moghani
  8. to appear in Kumomoto J. Math. (p,q,r)0Generation and nX-Complementary Generations of the Sporadic Group Ly M. R. Darafsheh;A. R. Ashrafi;G. A. Moghani
  9. (p,q,r)-Generation and nX-Complementary Generations of the Sporadic Group Ru M. R. Darafsheh;A. R. Ashrafi
  10. J. Algebra v.188 (p,q,r)-Generations of the smallest Conway group $Co_3$ S. Ganief;J. Moori
  11. J. Group Theory v.1 Generating pairs for the Conway groups $Co_2$ and $Co_3$ S. Ganief;J. Moori
  12. J. Algebra v.212 2-Generations of the Forth Janko Group $J_4$ S. Ganief;J. Moori
  13. J. Algebra v.188 (p,q,r)-Generations of the smallest Conway group $Co_3$ S. Ganief;J. Moori
  14. J. Algebra v.188 (p,q,r)-Generations and nX-complementary generations fo the sporadic groups HS and McL S. Ganief;J. Moori
  15. Nova J. Algebra and Geometry v.2 no.3 (p,q,r)-Generations for the Janko groups $J_1$ and $J_2$ J. Moori
  16. J. Algebra v.2 no.11 (2,3,p)-Generations for the Fischer group $F_22$ J. Moori
  17. Lehrstuhl De fur Mathematik CAP, Groups, Algorithms and Programming M. Schonert(et al.)
  18. J. Algebra v.144 Sporadic simple groups which are Hurwitz A. J. Woldar
  19. Illinois Math. J. v.33 no.3 On Hurwitz generation and genus actions of sporadic groups A. J. Woldar
  20. Korean J. Comput. and Appl. Math. v.7 The character table of the group $GL_2$(q) when extended by a certain group of order two M.R. Darafsheh;F. Nowroozi Larki
  21. Korean J. Comput. and Appl. Math. v.6 Equivalence of matrices in $GL_2$ (q) and $SL_2$(q) M.R. Darafsheh;F. Nowroozi Larki