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Disjoint conjugates of cyclic subgroups of finite groups
Published online by Cambridge University Press: 20 January 2009
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In an earlier paper (2) we considered the following question “If S is a cyclic subgroup of a finite group G and S ∩ F(G) = 1, where F(G) is the Fitting subgroup of G, does there necessarily exist a conjugate Sx of S in G with S ∩ Sx = l?” and we gave an affirmative answer for G simple or soluble. In this paper we answer the question affirmatively in general (in fact we prove a somewhat stronger result (Theorem 3)). We give an example of a group G with a cyclic subgroup S such that (i) no nontrivial subgroup of S is normal in G and (ii) no x exists for which S ∩ Sx = 1.
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- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 20 , Issue 3 , March 1977 , pp. 229 - 232
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- Copyright © Edinburgh Mathematical Society 1977
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