On cyclic subgroups of finite groups
1982 ◽
Vol 25
(1)
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pp. 19-20
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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).
1977 ◽
Vol 20
(3)
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pp. 229-232
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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)
◽
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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2009 ◽
Vol 52
(1)
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pp. 145-150
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