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- W2017654610 abstract "For any integer $n geq 2$, denote by ${R_n}$ the class of groups $G$ in which every infinite subset $X$ contains $n$ elements ${x_1}, ldots ,{x_n}$ such that the product ${x_1} ldots {x_n} = {x_{sigma (1)}} cdots {x_{sigma (n)}}$ for some permutation $sigma ne 1$. The case $n = 2$ was studied by B. H. Neumann who proved that ${R_2}$ is precisely the class of centre-by-finite groups. Here we show that $G in {R_n}$ for some $n$ if and only if $G$ contains an FC-subgroup $F$ of finite index such that the exponent of $F/Z(F)$ is finite, where $Z(F)$ denotes the centre of $F$." @default.
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- W2017654610 date "1992-08-01" @default.
- W2017654610 modified "2023-09-23" @default.
- W2017654610 title "Groups with Many Rewritable Products" @default.
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- W2017654610 doi "https://doi.org/10.2307/2159336" @default.
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