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

Short Communication

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

Stephen Kipkemoi Kibet1, Ireri N. Kamuti1, Gregory Kerich2 and Albert Kimutai3*
  1Department of Mathematics, Kenyatta University, P. O. Box 43844-00100 Nairobi, Kenya. 2Gregory Kerich, Mount Kenya University, Eldoret Campus P. O. Box 6212-30100, Eldoret Kenya. 3Kabianga University College, P. O. Box 2030-20200, Kericho, Kenya.
Email: [email protected]

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

Abstract

 

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) have been calculated by Higman (1970). He showed that the rank is 3 and the sub-degrees are. Therefore, we extend these calculations to the specific symmetric groups Sn (n≤7) acting on X (3).

 

Key words: Ranks, sub-degrees, suborbits, primitivity.