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On cyclic subgroups of finite groups
Published online by Cambridge University Press: 20 January 2009
Extract
In [3] Laffey has shown that if Z is a cyclic subgroup of a finite subgroup G, then either a nontrivial subgroup of Z is normal in the Fitting subgroup F(G) or there exists a g in G such that Zg∩Z = 1. In this note we offer a simple proof of the following generalisation of that result:
Theorem. Let G be a finite group and X and Y cyclic subgroups of G. Then there exists a g in G such that Xg∩Y⊴F(G).
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- Research Article
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- Proceedings of the Edinburgh Mathematical Society , Volume 25 , Issue 1 , February 1982 , pp. 19 - 20
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- Copyright © Edinburgh Mathematical Society 1982
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