Enumeration of finite groups / Simon R. Blackburn, Peter M. Neumann, Geetha Venkataraman.

Show other versions (2)

How many groups of order n are there? This is a natural question for anyone studying group theory, and this Tract provides an exhaustive and up-to-date account of research into this question spanning almost fifty years. The authors presuppose an undergraduate knowledge of group theory, up to and inc...

Full description

Bibliographic Details
Uniform Title:Cambridge tracts in mathematics ; 173.
Main Authors: Blackburn, Simon R. (Author)
Neumann, P. M. (Author)
Venkataraman, Geetha (Author)
Language:English
Published: Cambridge : Cambridge University Press, 2007.
Series:Cambridge tracts in mathematics ; 173.
Subjects:
Finite groups.
Online Access:
Connect to online resource - MSU authorized users (Digital Object Identifier Permalink)
Physical Description:1 online resource (xii, 281 pages) : digital, PDF file(s).
Format: Electronic eBook
Contents:
  • Some basic observations
  • Preliminaries
  • Enumerating p-groups: a lower bound
  • Enumerating p-groups: upper bounds
  • Some more preliminaries
  • Group extensions and cohomology
  • Some representation theory
  • Primitive soluble linear groups
  • The orders of groups
  • Conjugacy classes of maximal soluble subgroups of symmetric groups
  • Enumeration of finite groups with abelian Sylow subgroups
  • Maximal soluble linear groups
  • Conjugacy classes of maximal soluble subgroups of the general linear groups
  • Pyber's theorem: the soluble case
  • Pyber's theorem: the general case
  • Enumeration within varieties of abelian groups
  • Enumeration within small varieties of A-groups
  • Enumeration within small varieties of p-groups.