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- W4300629407 abstract "We deal with the following conjecture. If w is a group word and G is a finite group in which any nilpotent subgroup generated by w-values has exponent dividing e, then the exponent of the verbal subgroup w(G) is bounded in terms of e and w only. We show that this is true in the case where w is either the nth Engel word or the word [x^n,y_1,y_2,...,y_k] (Theorem A). Further, we show that for any positive integer e there exists a number k=k(e) such that if w is a word and G is a finite group in which any nilpotent subgroup generated by products of k values of the word w has exponent dividing e, then the exponent of the verbal subgroup w(G) is bounded in terms of e and w only (Theorem B)." @default.
- W4300629407 created "2022-10-03" @default.
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- W4300629407 date "2013-01-17" @default.
- W4300629407 modified "2023-09-26" @default.
- W4300629407 title "Bounding the Exponent of a Verbal Subgroup" @default.
- W4300629407 doi "https://doi.org/10.48550/arxiv.1301.4093" @default.
- W4300629407 hasPublicationYear "2013" @default.
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