Permutable word products in groups
1989 ◽
Vol 40
(2)
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pp. 243-254
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Let u(x1,…,xn) = x11 … x1m be a word in the alphabet x1, …,xn such that x1i ≠ x1i for all i = 1,…, m − 1. If (H1, …, Hn) is an n-tuple of subgroups of a group G then denote by u(H1, …, Hn) the set {u(h1,…,hn) | hi ∈ Hi}. If σ ∈ Sn then denote by uσ(H1,…,Hn) the set u(Hσ(1),…,Hσ(n)). We study groups G with the property that for each n-tuple (H1,…,Hn) of subgroups of G, there is some σ ∈ Sn σ ≠ 1 such that u(H1,…,Hn) = uσ(H1,…,Hn). If G is a finitely generated soluble group then G has this property for some word u if and only if G is nilpotent-by-finite. In the paper we also look at some specific words u and study the properties of the associated groups.
1978 ◽
Vol 19
(2)
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pp. 153-154
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Keyword(s):
1983 ◽
Vol 35
(2)
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pp. 218-220
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Keyword(s):
1981 ◽
Vol 31
(4)
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pp. 459-463
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1976 ◽
Vol 28
(6)
◽
pp. 1302-1310
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2000 ◽
Vol 61
(1)
◽
pp. 33-38
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Keyword(s):
2000 ◽
Vol 62
(1)
◽
pp. 141-148
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Keyword(s):
1994 ◽
Vol 50
(3)
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pp. 459-464
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2005 ◽
Vol 15
(02)
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pp. 273-277
2012 ◽
Vol 87
(1)
◽
pp. 152-157