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A finitary Tits' alternative

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Abstract.

It is shown that for any family of finite groups of uniformly bounded rank, either (i) a subdirect product of these groups contains a non-cyclic free group, or (ii) there exists a single word w which is a law in each group, and moreover, if N is the length of the word, and r the maximal rank of each finite group, then each group is nilpotent-of-bounded class-by-abelian-by-bounded-index, with the bounds being functions of N and r alone. Additionally, various corollaries are derived from this result.

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Authors and Affiliations

  1. Department of Mathematics, Hebrew University, Jerusalem 91904, Israel, , , , , , IL

    Sarah Black

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  1. Sarah Black
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Received: 22.8.1997

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Black, S. A finitary Tits' alternative. Arch. Math. 72, 86–91 (1999). https://doi.org/10.1007/s000130050308

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  • DOI: https://doi.org/10.1007/s000130050308

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