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Iranmanesh, Ali
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Mathematics

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Character Table Groups and Extracted Simple and Cyclic Polygroups Sekhavatizadeh, Sara; Zahedi, Mohammad Mehdi; Iranmanesh, Ali
Journal of the Indonesian Mathematical Society Volume 26 Number 1 (March 2020)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.26.1.742.22-36

Abstract

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.
Co-Authors Sekhavatizadeh, Sara Zahedi, Mohammad Mehdi