Abstract
An algorithm is given for computing soluble groups which is an extension of the nilpotent quotient algorithm. The method is based on the Reidemeister-Schreier method of presenting subgroups. Given G/G (k), where G/G (k) is the k-th term in the derived series we construct G (k)/G (k+1) and hence extend G/G (k) to G/G k+1). The problem of many generators is partially solved by introducing the notion of a module presentation.
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Reference
Wilhelm Magnus, Abraham Karrass, Donald Solitar, Combinatorial Group Theory: Presentations of groups in terms of generators and relations (Pure and Applied Mathematics, 13. Interscience [John Wiley & Sons], New York, London, Sydney, 1966). MR34#7617.
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© 1977 Springer-Verlag
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Wamsley, J.W. (1977). Computing soluble groups. In: Bryce, R.A., Cossey, J., Newman, M.F. (eds) Group Theory. Lecture Notes in Mathematics, vol 573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087817
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DOI: https://doi.org/10.1007/BFb0087817
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08131-9
Online ISBN: 978-3-540-37428-2
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