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

Journal of Mathematics and Statistics

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

Mohammed A. Al-Kadhi and Faryad Ali

DOI : 10.3844/jmssp.2012.339.341

Journal of Mathematics and Statistics

Volume 8, Issue 3

Pages 339-341

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.

Copyright

© 2012 Mohammed A. Al-Kadhi and Faryad Ali. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.