Properties of the symmetric groups Sn (n≤7) acting on unordered triples
Loading...
Date
2012-08
Authors
Kamuti, I.N.
Kibet, S. K.
Kerich, G.
Kimutai, A.
Journal Title
Journal ISSN
Volume Title
Publisher
African Journal of Mathematics and Computer Science Research
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).
Description
DOI: 10.5897/AJMCSR12.008
Keywords
Ranks, sub-degrees, suborbits, primitivity
Citation
African Journal of Mathematics and Computer Science Research Vol.5(10) , pp. 173-175 , August 2012