International Journal of Scientific & Technology Research

Home About Us Scope Editorial Board Blog/Latest News Contact Us
10th percentile
Powered by  Scopus
Scopus coverage:
Nov 2018 to May 2020


IJSTR >> Volume 3- Issue 12, December 2014 Edition

International Journal of Scientific & Technology Research  
International Journal of Scientific & Technology Research

Website: http://www.ijstr.org

ISSN 2277-8616

Intersection Matrices Associated With Non Trivial Suborbit Corresponding To The Action Of Rank 3 Groups On The Set Of Unordered Pairs

[Full Text]



BettyChepkorir, John K. Rotich, Benard C. Tonui, ReubenC. Langat



Index Terms: Intersection Matrices,Non Trivial Suborbit, Action of Rank 3 Groups,Set of Unordered Pairs



Abstract: In this paper we find intersection numbers and intersection matrices associated with each non trivial sub orbit corresponding to the action of rank 3 groups; The symmetric group S5,alternating group A5 and The dihedral group D5 on the set of unordered pairs. We showed that the column sum of the intersection matrices associated with is equal the length of the suborbit . They are also square matrices and of order 3x3.



[1] Akbas, M. 2001. Suborbital graphs for modular group, Bulletin of the London mathematical society 33:647-652.

[2] Burnside, W. 1911. Theory of groups of finite order, Cambridge University Press, Cambridge (Dover reprint 1955).

[3] Bon, J. V. and Cohen, A.M. 1989. Linear groups and distance-transitive groups, European Journal of combinatories 10:399-411.

[4] Cameron, P. J. 1972. Permutation groups with multiply transitive suborbitsI. Proc. London Math. Soc. 23 (3): 427 – 440.

[5] Cameron, P. J. 1974. Permutation groups with multiply transitive suborbits II. Bull. London Math. Soc. 6: 136 - 140.

[6] Cameron, P. J. 1978. Orbit of permutation groups on Unordered sets. J. London. Math. Soc. 17 (2): 410- 414.

[7] Chartrand, G. 1993. Applied and algorithmic graph theory. International series in pure and applied Mathematics: 238-240.

[8] Coxeter, H. S. M. 1986. My graph, proceedings of London mathematical society 46:117-136.

[9] Faradžev, I. A. and Ivanov, A. A. 1990. Distance-transitive representations of group G with PSL (2q)<-G< PTL (2,q), European journal of combinatories 11:347-356.

[10] Harary, F. 1969. Graph Theory. Addison – Wesley Publishing Company, New York.

[11] Higman, D. G. 1964. Finite permutation groups of rank 3. Math Zeitschriff 86: 145 – 156.

[12] Higman, D. G. 1970. Characterization of families of rank 3 permutation groups by subdegrees. I. Arch. Math 21: 151-156.

[13] Jones, G. A.; Singerman, D. and Wicks, K., 1991. Generalized Farey graphs in groups, St. Andrews 1989, Eds. C. Campbell and E.F. Robertson, London mathematical society lecture notes series 160, CambridgeUniversity, Cambridge 316 – 338.

[14] Kamuti, I. N. 1992. Combinatorial formulas, invariants and structures associated with primitive permutation representations of PSL (2, q) and PGL (2, q). Ph. D. Thesis, Southampton University, U.K.

[15] Kamuti, I. N. 2006. Subdegrees of primitive permutation representation of PGL (2,q), East African journal of physical sciences 7(1/2):25-41.

[16] Kangogo, M. 2008. Some properties of symmetric group S6 and associated combinatorial formulas and structures, M.SC. Project; Kenyatta, University, Kenya.

[17] Krishnamurthy, V. 1985. Combinatorics, theory and applications, Affliated East West Press Private Limited, New Delhi.

[18] Neumann, P. M. 1977. Finite permutation groups edge-coloured graphs and matrices edited by M. P. J. Curran, Academic Press, London.

[19] Petersen, J. 1898. Sur le. Theore’me de Tait Intermed Math 5:225-227.

[20] Rose, J. S. 1978. A Course on group theory. CambridgeUniversity Press, Cambridge.

[21] Rosen, K. H. 1999. Handbook of Discrete and combinational Mathematics. CRC Press, New Jersey.

[22] Rotman, J. J. 1973. The theory of groups: An introduction. Allyn and Bacon, Inc. Boston, U.S.A.

[23] Rotich, K. S. 2008. Some properties of the symmetric group S7 acting on ordered and unordered Pairs and the associated combinatorial structures, M.SC. Project, Kenyatta University,Kenya.

[24] Galois, C. 1830. Self-Conjugate sub-groups; simple and composite groups. CambridgeUniversity Press Cambridge.

[25] Jordan, C. 1870. Traite des substitutions et des Equations Algebriques. Gauthier – Villas, Paris.

[26] Sims, C. C. 1967. Graphs and finite permutation groups. Math. Zeitschrift 95: 76 – 86.

[27] Wielandt, H. 1964. Finite Permutation Groups. Academic Press, New York and London.