International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 62, Pages 3931-3948
doi:10.1155/S0161171203212023
Nested symmetric representation of elements of the Suzuki chain groups
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.
Abstract
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.