Journal of Advanced Mathematical Modeling

Journal of Advanced Mathematical Modeling

Powers of Irreducible Characters of Finite Groups

Authors
Mohammad Reza Darafsheh
Emad Zahedi
School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran
Abstract
Let  X  be an irreducible character of a non-abelian group  G. For non-negative integers n, m such that  m+n>0 , we study the case when all the irreducible constituents of XnXm  are linear. Mann proved that if  G is a finite non-abelian group with an irreducible character  X  such that all the irreducible constituents of
X2  are linear, then G<Z(G)  and as a consequence G is nilpotent. In this paper we generalize the result of Mann and prove that if m, n are non-negative integers with  m+n>0 , and if  X  is an irreducible character of G, then all the irreducible constituents of XnXm  are linear if and only if G<Z(G).
Keywords
Character
Finite Groups
Irreducible Character
Power
Product of Characters
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  • Receive Date 10 June 2013