Ranks, Subdegrees and Suborbital graphs of the product action of Affine Groups

Siahi Maxwell  Agwanda; Patrick  Kimani; Ireri  Kamuti

doi:10.24297/jam.v19i.8891

Authors

Siahi Maxwell Agwanda Department of Mathematics, Kenyatta University, P.O. Box 43844-00100, Nairobi
Patrick Kimani Department of Mathematics and Computer science, University of Kabianga, P.O. Box 2030-20200, Kericho
Ireri Kamuti Department of Mathematics, Kenyatta University, P.O. Box 43844-00100, Nairobi

DOI:

https://doi.org/10.24297/jam.v19i.8891

Keywords:

Transitivity and Suborbital graphs, Subdegrees, Ranks

Abstract

The action of affine groups on Galois field has been studied. For instance, studied the action of on Galois field for a power of prime. In this paper, the rank and subdegree of the direct product of affine groups over Galois field acting on the cartesian product of Galois field is determined. The application of the definition of the product action is used to achieve this. The ranks and subdegrees are used in determination of suborbital graph, the non-trivial suborbital graphs that correspond to this action have been constructed using Sims procedure and were found to have a girth of 0, 3, 4 and 6.

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References

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