Advertisement

Linear Methods in Nilpotent Groups

  • Bertram Huppert
  • Norman Blackburn
Chapter
  • 447 Downloads
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 242)

Abstract

The subject of this chapter is commutator calculation. It will be recalled that the commutator [x, y] of two elements x, y of a group is defined by the relation
$$ [x,y] = {{x}^{{ - 1}}}{{y}^{{ - 1}}}xy. $$
. We then have
$$ [xy,z] = {{[x,z]}^{y}}[y,z],\quad [x,yz] = [x,z]{{[x,y]}^{z}}. $$
. These relations are rather similar to the conditions for bilinearity of forms, and there are a number of ways of formalizing this similarity. Once this is done, commutator calculations can be done by linear methods. Several examples of theorems proved by this method will be given in this chapter.

Keywords

Linear Method Associative Algebra Nilpotent Group Central Series Invariant Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • Bertram Huppert
    • 1
  • Norman Blackburn
    • 2
  1. 1.Mathematisches Institut der UniversitätMainzGermany
  2. 2.Department of MathematicsThe UniversityGB-ManchesterUK

Personalised recommendations