Sara Sekhavatizadeh, Mohammad Mehdi Zahedi, Ali Iranmanesh


Let ${G}$ be a finite group and $\hat{G}$ be the set of all irreducible complex characters of $G.$ In this paper, we consider $<\hat{G}, *>$ as a polygroup, where for each $\chi _{i} ,\chi_{j}\in \hat{G}$ the product $\chi _{i} * \chi_{j}$ is the set of those irreducible constituents which appear in the element wise product $\chi_{i} \chi_{j}.$ We call that $\hat{G}$ simple if it has no proper normal subpolygroup and
show that if $\hat{G}$ is a single power cyclic polygroup, then $\hat{G}$ is a simple polygroup and hence $\hat{S}_{n}$ and $\hat{A}_{n}$ are simple polygroups. Also, we prove that if $G$ is a non-abelian simple group, then $\hat{G}$ is a single power cyclic polygroup. Moreover, we classify $\hat{D}_{2n}$ for all $n.$ Also, we prove that $\hat{T}_{4n}$ and $\hat{U}_{6n}$ are cyclic polygroups with finite period.


Character of group, hypergroup, polygroup, cyclic hyper- group, fundamental relation

Full Text:



Brauer, R. "{On pseudo groups}", {em J. Math. Soc. Japan}. 20 (1968),


Comer, S.D., "Hyperstructures associated with character algebra and color schemes", {em New Frontiers in Hyperstructures}, Hadronic Press, (1996) 49-66.

Corsini, P., {em Prolegomena of Hypergroup Theory}, ( Aviani Editore, Tricesimo), (1993).

Davvaz, B., {em Polygroup Theory and Related Systems}, World Scientific Publishing co. Pte. Ltd, (2013).

James. G., Liebeck. M, {em Representations and characters of groups}, Cambridge Univ. Press, (1993).

Konguetsof, L., Vougiouklis, T., Kessoglides, M. and Spartalis, S., "{ On cyclic hypergroups with period}", {em Acta Univ. Carolinae-Math. Physica.} 28 (1987), no 1, 3-7.

Leoreanu, V., "{ About the simplifiable cyclic semihypergroups}", {em Italian J. Pure Appl. Math.} 7 (2000), 69-76.

Mittas, J., "Hypergroupes canoniques hypervalues",(French), {em C. R. Acad. Sci. Paris Ser, A-B}, 271 (1970), A4- A-7.

Roth, R.L., "{ Character and conjugacy class hypergroups of a finite group}", {em Ann. Math. Pura Appl.} 105 (1975), 295-311.

Sekhavatizadeh, S., Zahedi, M.M. and Iranmanesh, A., "{ Cyclic hypergroups which are induced by the character of some finite groups}", {em Italian j. pure appl.} 33 (2014), 123-132.

Vougiouklis, T., "{ Cyclicity in a special class of hypergroups}", {em Acta Univ. Carolinae-Math.}

et Physica. 22 (1981), 3-6.

Wall, H.S., "{ Hypergroups}", {em Amer. J. Math.} 59 (1937), 77-98.



  • There are currently no refbacks.

Journal of the Indonesian Mathematical Society
Mathematics Department, Universitas Gadjah Mada
Senolowo, Sinduadi, Mlati, Sleman Regency, Special Region of Yogyakarta 55281, Telp. (0274) 552243

p-ISSN: 2086-8952 | e-ISSN: 2460-0245

Journal of the Indonesian Mathematical Society is licensed under a Creative Commons Attribution 4.0 International License

web statistics
View My Stats