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Semilinear and Skew Linear Groups

  • B. A. F. WehrfritzEmail author
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Part of the Algebra and Applications book series (AA, volume 10)

Abstract

In Chap. 4 we studied a polycyclic group by considering it as a subgroup of some GL(n,Z). Is there some sort of analogous way of obtaining properties of finitely generated abelian-by-polycyclic groups? Firstly a consideration of linear groups will not suffice, since soluble linear groups must be nilpotent-by-abelian-by-finite. Indeed not even all finitely generated, abelian-by-polycyclic, nilpotent-by-abelian-by-finite groups (that is, in the notation of Chap. 1, GAPNAF groups) need be isomorphic to even quasi-linear groups (a quasi-linear group is a subgroup of a direct product of a finite number of linear groups; equivalently a quasi-linear group is any group of automorphisms of a Noetherian module over a commutative ring, see Wehrfritz 1979c, p. 55).

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References

  1. Wehrfritz BAF (1979c) Lectures around complete local rings. Queen mary college math notes, London Google Scholar

Copyright information

© Springer-Verlag London 2009

Authors and Affiliations

  1. 1.School of Mathematical SciencesQueen Mary, University of LondonLondonUK

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