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Proceedings of the American Mathematical Society

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

 

 

A counterexample in the theory of finite groups


Author: David A. Sibley
Journal: Proc. Amer. Math. Soc. 69 (1978), 19-20
MSC: Primary 20C15; Secondary 20D99
DOI: https://doi.org/10.1090/S0002-9939-1978-0486089-0
MathSciNet review: 0486089
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Abstract: Suppose G is a finite group and p and q are distinct odd primes. Let $ \chi $ be an irreducible character of G and x and y be a p-element and a q-element of G such that $ \chi (x),\chi (y)$ are both irrational. In this situation it is known that G contains an element of order pq. John Thompson has asked whether y must commute with some conjugate of x. We show by example that this need not be the case.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0486089-0
Article copyright: © Copyright 1978 American Mathematical Society