A counterexample in the theory of finite groups
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- by David A. Sibley PDF
- Proc. Amer. Math. Soc. 69 (1978), 19-20 Request permission
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.References
- H. F. Blichfeldt, On the order of linear homogeneous groups. II, Trans. Amer. Math. Soc. 5 (1904), no. 3, 310–325. MR 1500676, DOI 10.1090/S0002-9947-1904-1500676-6
- W. Burnside, Theory of groups of finite order, Dover Publications, Inc., New York, 1955. 2d ed. MR 0069818
- Walter Feit, Characters of finite groups, W. A. Benjamin, Inc., New York-Amsterdam, 1967. MR 0219636
Additional Information
- © Copyright 1978 American Mathematical Society
- 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