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• W3100851290 abstract "We prove that outer commutator words are uniformly concise, that is, if an outer commutator word ω takes m different values in a group G, then the order of the verbal subgroup ω(G) is bounded by a function depending only on m, and not on ω or G. This is obtained as a consequence of a structure theorem for the subgroup ω(G), which is valid if G is soluble, and without assuming that ω takes finitely many values in G. More precisely, there is an abelian series of ω(G), such that every section of the series can be generated by values of ω all of whose powers are also values of ω in that section. For the proof of this latter result, we introduce a new representation of outer commutator words by means of binary trees, and we use the structure of the trees to set up an appropriate induction." @default.
• W3100851290 created "2020-11-23" @default.
• W3100851290 creator A5005996108 @default.
• W3100851290 creator A5072528984 @default.
• W3100851290 date "2010-09-15" @default.
• W3100851290 modified "2023-09-26" @default.
• W3100851290 title "Outer commutator words are uniformly concise" @default.
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• W3100851290 doi "https://doi.org/10.1112/jlms/jdq047" @default.
• W3100851290 hasPublicationYear "2010" @default.
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