Character Table Groups and Extracted Simple and Cyclic Polygroups - Sara Sekhavatizadeh; Mohammad Mehdi Zahedi; Ali Iranmanesh (IndoMS, 2020)
Let G be a finite group and G be the set of all irreducible complex characters of G. In this paper, we consider <G, *> as a polygroup, where for each chi_i ,chi_j in G the product χ _i * χ_j is the set of those irreducible constituents which appear in the element-wise product χ_i χ_j. We call that G simple if it has no proper normal subpolygroup and show that if G is a single power cyclic polygroup, then G is a simple polygroup and hence S_n and A_n are simple polygroups. Also, we prove that if G is a non-abelian simple group, then G is a single power cyclic polygroup. Moreover, we classify D_2n for all n. Also, we prove that T_4n and U_6n are cyclic polygroups with finite period.