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Transposable character tables and group duality

Published online by Cambridge University Press:  28 April 2014

IVAN ANDRUS ,
PÁL HEGEDŰS  and
TETSURO OKUYAMA
IVAN ANDRUS
Affiliation:
Department of Mathematics and its Applications, Central European UniversityNador utca 9, 1051 Budapest, Hungary. e-mail: Andrus_Ivan@ceu-budapest.edu, HegedusP@ceu.hu
PÁL HEGEDŰS
Affiliation:
Department of Mathematics and its Applications, Central European UniversityNador utca 9, 1051 Budapest, Hungary. e-mail: Andrus_Ivan@ceu-budapest.edu, HegedusP@ceu.hu
TETSURO OKUYAMA
Affiliation:
Laboratory of Mathematics, Hokkaido University of Education, Asahikawa, Hokkaido 070-0825, Japan. e-mail: okuyama.tetsuro@a.hokkyodai.ac.jp
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Abstract

One way of expressing the self-duality $A\cong {\rm Hom}(A,\mathbb{C})$ of Abelian groups is that their character tables are self-transpose (in a suitable ordering). In this paper we extend the duality to some noncommutative groups considering when the character table of a finite group is close to being the transpose of the character table for some other group. We find that groups dual to each other have dual normal subgroup lattices. We show that our concept of duality cannot work for non-nilpotent groups and we describe p-group examples.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 157 , Issue 1 , July 2014 , pp. 31 - 44
Copyright
Copyright © Cambridge Philosophical Society 2014 

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