Journal of Formalized Mathematics
Volume 3, 1991
University of Bialystok
Copyright (c) 1991 Association of Mizar Users

Commutator and Center of a Group


Wojciech A. Trybulec
Warsaw University, Bialystok

Summary.

We introduce the notions of commutators of element, subgroups of a group, commutator of a group and center of a group. We prove P.Hall identity. The article is based on [5].

MML Identifier: GROUP_5

The terminology and notation used in this paper have been introduced in the following articles [8] [16] [3] [1] [2] [4] [14] [9] [10] [6] [12] [15] [11] [13] [7]

Contents (PDF format)

  1. Preliminaries
  2. Commutators
  3. Center of a Group
  4. Auxiliary theorems

Bibliography

[1] Grzegorz Bancerek. Cardinal numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[3] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[4] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[5] M. I. Kargapolow and J. I. Mierzlakow. \em Podstawy teorii grup. PWN, War\-sza\-wa, 1989.
[6] Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski. Abelian groups, fields and vector spaces. Journal of Formalized Mathematics, 1, 1989.
[7] Andrzej Trybulec. Domains and their Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[8] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[9] Michal J. Trybulec. Integers. Journal of Formalized Mathematics, 2, 1990.
[10] Wojciech A. Trybulec. Vectors in real linear space. Journal of Formalized Mathematics, 1, 1989.
[11] Wojciech A. Trybulec. Classes of conjugation. Normal subgroups. Journal of Formalized Mathematics, 2, 1990.
[12] Wojciech A. Trybulec. Groups. Journal of Formalized Mathematics, 2, 1990.
[13] Wojciech A. Trybulec. Lattice of subgroups of a group. Frattini subgroup. Journal of Formalized Mathematics, 2, 1990.
[14] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[15] Wojciech A. Trybulec. Subgroup and cosets of subgroups. Journal of Formalized Mathematics, 2, 1990.
[16] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.

Received May 15, 1991

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