Patrick Mwangi Kimani, Ireri Kamuti, Jane Rimberia. (2019). Rank and Subdegrees of P GL (2, q) Acting Cosets of P GL (2, e) for q an Even Power of e. International Journal of Algebra, 13(1): 29-36, ISSN: 1314-7595 (online) ISSN: 1312-8868 (print).
Gikunju David Muriuki, Nyaga Lewis Namu and Rimberia Jane Kagwiria. (2017). Ranks, Subdegrees and Suborbital graphs of Direct Product of the Symmetric group acting on Cartesian product of three sets. Pure and Applied Mathematical Journal , 6(1): 1-4, ISSN 2326-9790 (Print) ISSN 2326 -9812 (Online).
R. Gachimu, I. Kamuti, L. Nyaga, J. Rimberia and P. Kamaku. (2016). Properties and invariants associated with the action of the alternating group on unordered subsets International Journal of Pure and Applied Mathematics, 106(1): 333-346 ISSN: 1311-8080 (Print); ISSN: 1314-33 (Online).
Richard Gachimu, Ireri Kamuti, Lewis Nyaga and Jane Rimberia. (2015). On the suborbits of the alternating group an acting on ordered r−element, International Electronic Journal of Pure and Applied Mathematics, 9(3): 137-14, ISSN: 1314-0744.
Gachago J., Kinyanjui J. , Kimani P., Rimberia J., Kiboi J. 2015. Transitivity of the action of Alternating group acting on Ordered and Unordered quadruples. Journal of Mathematical Theory and Modeling, 5:6 111-123 ISSN 2224-5804(Print) ISSN 2225-0522 (Online).
- J. K. Rimberia, I. N. Kamuti. 2015 Subgroups of the Orthogonal Group in three dimensions and their Poles. International Journal of Mathematics and Statics Studies (European Centre for Research Training and Development UK) Vol.3, No.1, pp.27-42, ISSN 2053-2229 (Print), ISSN 2053-2210 (Online)
- J. K. Rimberia, I. N. Kamuti. 2015. Subdegrees of Primitive permutation representations of the Symmetric Group. International Journal of Scientific Research and Innovative Technology, Vol. 2 , No. 4 pp. 26-33, ISSN: 2313-3759 (Online)
- 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.