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The Basic Theory of Polycyclic Groups

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

Abstract

Group Classes

This is effectively just a language, developed by P.Hall in the 1950’s and 60’s to make certain types of group theoretic arguments more concise while highlighting the essential components of the proof.

A group class is a class X of groups such that H GX implies HX (the main condition; effectively we are dealing with isomorphism classes of groups rather than the groups themselves) and such that 〈1〉∈X (a convenient convention). For certain commonly used classes we have special notations. These include the following.

Keywords

Normal Subgroup Basic Theory Isomorphism Class Nilpotent Group Closure Operator 
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.

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Copyright information

© Springer-Verlag London 2009

Authors and Affiliations

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

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