African Journal of
Mathematics and Computer Science Research

  • Abbreviation: Afr. J. Math. Comput. Sci. Res.
  • Language: English
  • ISSN: 2006-9731
  • DOI: 10.5897/AJMCSR
  • Start Year: 2008
  • Published Articles: 254

Full Length Research Paper

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

Stephen Kipkemoi Kibet1, Kimutai Albert2* and Kandie Joseph3
  1Department of Mathematics, Kenyatta University, P. O. Box 43844-00100 Nairobi, Kenya. 2Kabianga University College, P. O. Box 2030-20200, Kericho, Kenya. 3Mathematics and Computer Science Department, Chepkoilel University College, P.O. Box 1125-30100, Eldoret.  
Email: [email protected]

  •  Accepted: 06 February 2012
  •  Published: 31 August 2012

Abstract

 

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 Harary (1969) in Cauchy-Frobenius Lemma and hence deduce transitivity.

 

Key words: Cycles, | Fix (g) |, Lemma.