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- W4302584188 abstract "A BFC-group is a group in which all conjugacy classes are finite with bounded size. In 1954 B. H. Neumann discovered that if G is a BFC-group then the derived group G' is finite. Let w=w(x_1,dots,x_n) be a multilinear commutator. We study groups in which the conjugacy classes containing w-values are finite of bounded order. Let G be a group and let w(G) be the verbal subgroup of G generated by all w-values. We prove that if x^G has size at most m for every w-value x, then the derived subgroup of w(G) is finite of order bounded by a function of m and n. If x^{w(G)} has size at most m for every w-value x, then [w(w(G)),w(G)] is finite of order bounded by a function of m and n." @default.
- W4302584188 created "2022-10-06" @default.
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- W4302584188 date "2018-03-12" @default.
- W4302584188 modified "2023-10-16" @default.
- W4302584188 title "BFC-theorems for higher commutator subgroups" @default.
- W4302584188 doi "https://doi.org/10.48550/arxiv.1803.04202" @default.
- W4302584188 hasPublicationYear "2018" @default.
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