Title/Qualifications: Doctor, PhD in Pure Mathematics
Department/Unit/Section: Mathematics Department
Contact Address: P.O.BOX 43844, 00100 Nairobi
Area of Specialization: Algebra
Research Interests: Combinatorics
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- J. K. Rimberia, I. N. Kamuti, B. M. Kivunge and F. Kinyua. (2013). Properties of Suborbits and Suborbital graphs of the Symmetric group acting on ordered r-element subsets, Journal of Mathematical Theory and Modeling, 3:11, 115-120.
- J. K. Rimberia, I. N. Kamuti, B. M. Kivunge and F. Kinyua. (2013). Subdegrees of the Symmetric Group acting acting on ordered r-element subsets, International journal of Science, Commerce and Humanities 1: 6, 112-118.
- I. N. Kamuti, E .B. Inyangala and J. K. Rimberia. (2012). Action of on and the corresponding Suborbital graphs, International Mathematical Forum, 7: 30, 1483-1490.
- Kinyanjui J. N., Musundi S. W., Rimberia J., Sitati N. I. and Makila P., 2013,Transitivity of the action of on Unordered and Ordered pairsInternational Journal of Mathematical Archive, Vol.4, No. 9 pg. 77-88ISSN 2229 – 5046
- Conference Presentations
- Dr. Jane Rimberia, Ranks and subdegrees of the symmetric group acting on ordered r-element subsets, Nairobi, Kenya, 8th- 10th June 2011
ONGOING RESEARCH WORK
Orbits of finite subgroups of the Orthogonal Group in three dimensions
An orthogonal group of a vector space V, denoted (V), is the group of all orthogonal transformations of V under the binary operation of composition of maps. If , then det and i.e. the inverse of T equals its transpose.
The well-known finite subgroups of the orthogonal group in three dimensions are: the cyclic groups Cn; the dihedral group of degree n, Dn; the alternating group of degree 4, A4; the symmetric group of degree 4, S4 and the alternating group of degree 5, A5.
In this research we determine the number of orbits in the action of finite subgroups of the orthogonal group in three dimensions on the set of their poles using table of marks. Group Algorithms and Programming (GAP) software will be used to generate tables of marks and solve the resulting systems of linear equations.