Research Article Open Access

On (2, 3, t)-Generations for the Conway Group Co2

Mohammed A. Al-Kadhi1 and Faryad Ali1
  • 1 Al-Imam Mohammed Bin Saud Islamic University, Saudi Arabia

Abstract

Problem statement: In this article we investigate all the (2, 3, t)-generations for the Conway’s second largest sporadic simple group Co2, where t is an odd divisor of order of Co2. Approach: An (l, m, n)-generated group G is a quotient group of the triangle group T (l, m, n) = (x, y, z|x1 = ym = zn = xyz = 1). A group G is said to be (2, 3, t)-generated if it can be generated by two elements x and y such that o(x) = 2, o(y) = 3 and o (xy) = t. Computations are carried out with the aid of computer algebra system GAP-Groups, Algorithms and Programming. Results and Conclusion: The Conway group Co2 is (2, 3, t)-generated for t an odd divisor of order of Co2 except when t = 5, 7, 9.

Journal of Mathematics and Statistics
Volume 8 No. 3, 2012, 339-341

DOI: https://doi.org/10.3844/jmssp.2012.339.341

Submitted On: 8 April 2012 Published On: 31 August 2012

How to Cite: Al-Kadhi, M. A. & Ali, F. (2012). On (2, 3, t)-Generations for the Conway Group Co2. Journal of Mathematics and Statistics, 8(3), 339-341. https://doi.org/10.3844/jmssp.2012.339.341

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Keywords

  • Conway group
  • sporadic simple group
  • generation
  • subject classification
  • sporadic group