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

Published online by Cambridge University Press:  20 November 2018

S. K. Prajapati  and
R. Sarma
S. K. Prajapati
Affiliation:
Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016, INDIA e-mail: skprajapati.iitd@gmail.com e-mail: ritumoni@maths.iitd.ac.in
R. Sarma
Affiliation:
Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016, INDIA e-mail: skprajapati.iitd@gmail.com e-mail: ritumoni@maths.iitd.ac.in
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Abstract

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We investigate whether the total character of a finite group $G$ is a polynomial in a suitable irreducible character of $G$ . When $\left( G,\,Z\left( G \right) \right)$ 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 $Z\left( G \right)$ is cyclic.

Keywords

20C15finite groupsgroup characterstotal characters
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 59 , Issue 2 , 01 June 2016 , pp. 392 - 402
Copyright
Copyright © Canadian Mathematical Society 2016

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