Bulletin of the Iranian Mathematical Society

, Volume 45, Issue 5, pp 1515–1529 | Cite as

Camina Triples and the Wedge Product of Association Schemes

  • Javad BagherianEmail author
Original Paper


In this paper, we first show that the group scheme of a Camina triple has the wedge product structure of association schemes. Then as a main result, we give a characterization of Camina triples in terms of their irreducible characters.


Association scheme Camina triple Character Wedge product 

Mathematics Subject Classification

20C99 05E30 



  1. 1.
    Bagherian, J.: On the multiplicities of characters in table algebras. Can. Math. Bull. 57, 231–239 (2014)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bannai, E., Ito, T.: Algebraic Combinatorics I: Association Schemes. Benjamin/Cummings, Menlo Park (1984)zbMATHGoogle Scholar
  3. 3.
    Bannai, E.: Subschemes of some association schemes. J. Algebra 144, 167–188 (1991)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Blau, H.I., Xu, B.: Irreducible characters of wreath products in reality-based algebras and applications to association schemes. J. Algebra 412, 155–172 (2014)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Camina, A.R.: Some conditions which almost characterize Frobenius groups. Israel J. Math. 31, 153–160 (1978)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Hanaki, A.: Representations of association schemes and their factor schemes. Graphs Combin. 19, 195–201 (2003)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Isaacs, M.: Character Theory of Finite Groups. Dover, New York (1994)zbMATHGoogle Scholar
  8. 8.
    Johnson, K.W., Mattarei, S., Sehgal, S.K.: Weak Cayley tables. J. Lond. Math. Soc. 61(2), 395–411 (2000)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Lewis, M.L.: Generalizing Camina groups and their character tables. J. Group Theory 12, 209–218 (2009)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Lewis, M. L.: Character tables of groups where all nonlinear irreducible characters vanish off the center. In: Proceeding of Ischia Group Theory, pp. 174–182 (2008)Google Scholar
  11. 11.
    Muzychuk, M.: A wedge product of association schemes. Eur. J. Combin. 30, 705–715 (2009)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Zieschang, P.-H.: An Algebraic Approach to Association Schemes. In: Lect. Notes in Math., vol. 1628, Springer, Berlin (1996)CrossRefGoogle Scholar

Copyright information

© Iranian Mathematical Society 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IsfahanIsfahanIran

Personalised recommendations