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Total Character of a Group $G$ with $(G,Z(G))$ as a Generalized Camina Pair

  Published:2016-01-28
 Printed: Jun 2016
  • S. K. Prajapati,
    Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016, INDIA
  • R. Sarma,
    Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016, INDIA
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Abstract

We investigate whether the total character of a finite group $G$ is a polynomial in a suitable irreducible character of $G$. When $(G,Z(G))$ is a generalized Camina pair, we show that the total character is a polynomial in a faithful irreducible character of $G$ if and only if $Z(G)$ is cyclic.
Keywords: finite groups, group characters, total characters finite groups, group characters, total characters
MSC Classifications: 20C15 show english descriptions Ordinary representations and characters 20C15 - Ordinary representations and characters
 

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