Ranks, Subdegrees and Suborbital Graphs of Direct Product of the Symmetric Group Acting on the Cartesian Product of Three Sets
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Date
2017-02
Authors
Gikunju, David Muriuki
Nyaga, Lewis Namu
Rimberia, Jane Kagwiria
Journal Title
Journal ISSN
Volume Title
Publisher
science publishing group
Abstract
Transitivity and Primitivity of the action of the direct product of the symmetric group on Cartesian product of
three sets are investigated in this paper. We prove that this action is both transitive and imprimitive for all n ³ 2 . In addition,
we establish that the rank associated with the action is a constant 3 2 .
Further; we calculate the subdegrees associated with the
action and arrange them according to their increasing magnitude.
Description
article
Keywords
Direct Product, Symmetric Group, Action, Rank, Subdegrees, Cartesian Product, Suborbit
Citation
Gikunju David Muriuki, Nyaga Lewis Namu, Rimberia Jane Kagwiria. Ranks, Subdegrees and Suborbital Graphs of Direct Product of the Symmetric Group Acting on the Cartesian Product of Three Sets. Pure and Applied Mathematics Journal. Vol. 6, No. 1, 2017, pp. 1-4. doi: 10.11648/j.pamj.20170601.11