Powers of Irreducible Characters of Finite Groups

Authors

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).

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References

[1] Isaacs, I.M. (1976), Character theory of finite groups, Academic press, Inc., New York.
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History

  • Receive Date: 10 June 2013
  • Accept Date: 10 June 2013

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