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Journal of Mathematical Sciences

, Volume 83, Issue 5, pp 673–679 | Cite as

The foundations of enumeration theory for finite nilpotent groups

  • V. N. Shokuev
Article
  • 19 Downloads

Abstract

This paper is the first in a series of papers that lay the foundations of enumeration theory for finite groups including the classical inversion calculus on segments of the natural series and on lattices of subsets of finite sets. Since it became possible to calculate the Möbius function on all subgroups of finite nilpotent groups, the Möbius inversion on these groups began to play a decisive role. The efficiency of the inversion method as a regular technique suitable for solution of enumeration problems of group theory is illustrated with a number of concrete and very important enumerations. Bibliography: 13 titles.

Keywords

Finite Group Maximal Subgroup Nilpotent Group Majorant Subgroup Gauss Coefficient 
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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© Plenum Publishing Corporation 1997

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  • V. N. Shokuev

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