International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 62, Pages 3931-3948

Nested symmetric representation of elements of the Suzuki chain groups

Mohamed Sayed

Department of Mathematics and Computer Science, Faculty of Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

Received 2 December 2002

Copyright © 2003 Mohamed Sayed. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We demonstrate an economic and concise method for representing the elements of groups involved in the Suzuki chain. For example, we represent each element of Suz:2 by a permutation on 14 letters from L3(2):2 followed by four words, each of length at most two, in 14, 36, 100, and 416 involutory symmetric generators, respectively. Such expressions will have an obvious advantage over permutations on 1782 provided that it is reasonably simple to multiply and invert them. We refer to this as nested symmetric representation of an element of the group.