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]

Preliminaries

Commutators

Center of a Group

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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