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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On certain groups of central type


Author: Alberto Espuelas
Journal: Proc. Amer. Math. Soc. 97 (1986), 16-18
MSC: Primary 20C15; Secondary 20D15
DOI: https://doi.org/10.1090/S0002-9939-1986-0831377-3
MathSciNet review: 831377
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Abstract: A finite group $ G$ is a group of central type if there exists $ \chi \in {\text{Irr}}\left( G \right)$ with $ \chi {\left( 1 \right)^2} = \left\vert {G:Z\left( G \right)} \right\vert$. It is known that, in such conditions, $ G$ is solvable. Here some conditions assuring the nilpotence of groups of central type are given.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0831377-3
Article copyright: © Copyright 1986 American Mathematical Society