Semilinear and Skew Linear Groups

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


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).


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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

Personalised recommendations