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• W1982714209 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 $$ntext{ th }$$ Engel word or the word $$[x^n,y_1,y_2,ldots ,y_k]$$ (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.
• W1982714209 created "2016-06-24" @default.
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• W1982714209 date "2013-04-04" @default.
• W1982714209 modified "2023-10-13" @default.
• W1982714209 title "Bounding the exponent of a verbal subgroup" @default.
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• W1982714209 doi "https://doi.org/10.1007/s10231-013-0336-8" @default.
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