August 2012

Results of symmetric groups Sn (n≤7) acting on unordered triples and ordered quadruples

  In this paper, we examined the results of fixed point set of symmetric groups Sn (n≤7) acting on X (3)   and X [4]. In order to find the fixed point set| fix (g) | of these permutation groups, we used the method developed by Higman (1970) to compute the number of orbits, ranks and sub degrees of these actions. The results were used to find the number of orbits as proposed by...

Author(s): Stephen Kipkemoi Kibet, Kimutai Albert and Kandie Joseph

August 2012

Properties of the symmetric groups Sn (n≤7) acting on unordered triples

  In this paper, we investigated some properties associated with the action of symmetric group Sn (n≤7) acting on X(3). If Gx is the stabilizer of , the lengths of the orbits of Gx on X are called sub-degrees and the numbers of orbits are called ranks. Ranks and sub-degrees of symmetric groups Sn (n=1, 2, ----) acting on 2-elements subsets from the set X= (1, 2, ---, n)...

Author(s): Stephen Kipkemoi Kibet, Ireri N. Kamuti, Gregory Kerich and Albert Kimutai