The structure of groups whose subgroups are permutable-by-finite
2006 ◽
Vol 81
(1)
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pp. 35-48
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AbstractA subgroup H of a group G is said to be permutable if HX = XH for each subgroup X of G, and the group G is called quasihamiltonian if all its subgroups are permutable. We shall say that G is a Q F-group if every subgroup H of G contains a subgroup K of finite index which is permutable in G. It is proved that every locally finite Q F-group contains a quasihamiltonian subgroup of finite index. In the proof of this result we use a theorem by Buckley, Lennox, Neumann, Smith and Wiegold concerning the corresponding problem when permutable subgroups are replaced by normal subgroups: if G is a locally finite group such that H/HG is finite for every subgroup H, then G contains an abelian subgroup of finite index.
1987 ◽
Vol 36
(3)
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pp. 461-468
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2007 ◽
Vol 49
(2)
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pp. 411-415
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2013 ◽
Vol 89
(3)
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pp. 479-487
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1996 ◽
Vol 60
(2)
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pp. 222-227
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2005 ◽
Vol 04
(02)
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pp. 165-171
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