caa a22 4500 38636009X CHVBK 20180307111912.0 cr unu---uuuuu 161130e198910 xx s 000 0 eng 10.1017/S0004972700004354 doi S0004972700004354 pii (NATIONALLICENCE)cambridge-10.1017/S0004972700004354 Permutable word products in groups [Elektronische Daten] 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. Copyright © Australian Mathematical Society 1989 Kim P.S. Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1 Rhemtulla A.H. Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1 Bulletin of the Australian Mathematical Society Cambridge University Press 40/2(1989-10), 243-254 0004-9727 40:2<243 1989 40 BAZ https://doi.org/10.1017/S0004972700004354 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0004972700004354 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kim P.S. Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1 NATIONALLICENCE 700 1- Rhemtulla A.H. Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1 NATIONALLICENCE 773 0- Bulletin of the Australian Mathematical Society Cambridge University Press 40/2(1989-10), 243-254 0004-9727 40:2<243 1989 40 BAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge