Disjoint conjugates of cyclic subgroups of finite groups
1977 ◽
Vol 20
(3)
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pp. 229-232
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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.
1982 ◽
Vol 25
(1)
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pp. 19-20
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2014 ◽
Vol 13
(04)
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pp. 1350141
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2008 ◽
Vol 01
(03)
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pp. 369-382
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2019 ◽
Vol 19
(04)
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pp. 2050073
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1977 ◽
Vol 20
(3)
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pp. 225-228
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2012 ◽
Vol 49
(3)
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pp. 390-405
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2013 ◽
Vol 88
(3)
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pp. 448-452
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2009 ◽
Vol 52
(1)
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pp. 145-150
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Keyword(s):
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