Nested symmetric representation of elements of the Suzuki chain groups

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.