On the Irreducible Characters of Camina Triples

Author
University of Isfahan
Abstract
The Camina triple condition is a generalization of the Camina condition in the theory of finite groups. The irreducible characters of Camina triples have been verified in the some special cases. In this paper, we consider a Camina triple (G,M,N) and determine the irreducible characters of G in terms of the irreducible characters of M and G/N../files/site1/files/61/0Abstract(1).pdf
Keywords

1. Bagherian J., "A class of imprimitive association schemes", Comm. Algebra, 44 (2016) 3692-3704. ## 2. Bannai E., Ito T., "Algebraic Combinatorics I: Association Schemes", Benjamin/Cummings, Menlo Park (1984). ## 3. Bannai E., "Subschemes of some association schemes", J. Algebra, 144 (1991) 167-188. ## 4. French C., Zieschang P. H., "A Schur–Zassenhaus Theorem for association schemes", J. Algebra, 435 (2015) 88-123. ## 5. Hanaki A., "Clifford theory for association schemes", J. Algebra, 321 (2009) 1686-1695. ## 6. Hirasaka M., Muzychuk M., Zieschang P. H., "A generalization of Sylow’s theorems on finite groups to association schemes", Math. Z., 241 (2002) 665-672. ## 7. Isaacs I. M., "Character Theory of Finite Groups", Academic Press, New York (1976). ## 8. Johnson K. W., Mattarei S., Sehgal S. K., "Weak Cayley tables", J. London Math. Soc., (2) 61 (2000) 395-411## 9. Lewis M. L., "Generalizing Camina groups and their character tables", J. Group Theory, 12 (2009) 209-218. ## 10. Lewis M. L., "Character tables of groups where all nonlinear irreducible characters vanish off the center", in: Proceeding of Ischia Group Theory, (2008) 174-182. ## 11. Zieschang P. H., "An Algebraic Approach to Association Schemes", in: Lect. Notes in Math., vol. 1628, Springer-Verlag, Berlin (1996). ## 12. Zieschang P. H., "Theory of Association Schemes", Springer Monographs in Mathematics, Springer-Berlin (2005). ##