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A formal power series attached to a class function on a group and its application to the characterisation of characters

Published online by Cambridge University Press:  03 July 2013

KENNETH W. JOHNSON  and
EIRINI POIMENIDOU
KENNETH W. JOHNSON
Affiliation:
Abington College, The Pennsylvania State University, 1600 Woodland Road, Abington, PA 19001, U.S.A. e-mail: kwj1@psu.edu
EIRINI POIMENIDOU
Affiliation:
Division of Natural Sciences, New College of Florida, 5800 Bay Shore Road, Sarasota, FL 34243, U.S.A. e-mail: poimenidou@ncf.edu
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Abstract

In Frobenius' initial papers on group characters he introduced k-characters in order to give an algorithm to calculate the irreducible factors of the group determinant. We show how his work leads naturally to the construction of a formal power series for any class function on a group, which terminates if and only if the class function is a character. This is then used to obtain a criterion for a class function to be a character.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 155 , Issue 3 , November 2013 , pp. 465 - 474
Copyright
Copyright © Cambridge Philosophical Society 2013 

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