The foundations of enumeration theory for finite nilpotent groups
- 19 Downloads
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.
KeywordsFinite Group Maximal Subgroup Nilpotent Group Majorant Subgroup Gauss Coefficient
Unable to display preview. Download preview PDF.
- 2.Enumeration Problems of Combinatorial Analysis [Russian translation], Mir, Moscow (1979).Google Scholar
- 3.M. Hall,Group Theory [Russian translation], Mir, Moscow (1962).Google Scholar
- 4.T. A. Tsaturyan and V. N. Shokuev, “On some relations between group-theoretic invariants of finitep-groups. II,” in:Algebra and Number Theory [in Russian], Nal'chik (1977), pp. 139–146.Google Scholar
- 5.O. Yu. Shmidt,Selected Papers. Mathematics [in Russian], Moscow (1959).Google Scholar
- 7.V. N. Shokuev, “On the number of subgroups of a finitep-group,”Mat. Zap. Ural'skogo Univ.,8, No. 3, 133–138 (1972).Google Scholar
- 11.V. N. Shokuev, “Enumeration theory for finite nilpotent groups,” Abstracts on group theory, Intern. Conf. on Algebra, Novosibirsk (1991).Google Scholar