Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
Classes of Conjugation. Normal Subgroups

Wojciech A. Trybulec

Warsaw University

Supported by RPBP.III24.C1.
Summary.

Theorems that were not proved in [13]
and in [14] are discussed. In the article we define notion of conjugation
for elements, subsets and subgroups of a group. We define the classes of
conjugation. Normal subgroups of a group and normalizator of a subset of a
group or of a subgroup are introduced. We also define the set of all subgroups
of a group. An auxiliary theorem that belongs rather to [2] is
proved.
MML Identifier:
GROUP_3
The terminology and notation used in this paper have been
introduced in the following articles
[10]
[6]
[15]
[3]
[16]
[4]
[5]
[12]
[7]
[8]
[14]
[9]
[1]
[11]
[13]
Contents (PDF format)
Bibliography
 [1]
Grzegorz Bancerek.
Cardinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Grzegorz Bancerek.
Cardinal arithmetics.
Journal of Formalized Mathematics,
2, 1990.
 [3]
Czeslaw Bylinski.
Binary operations.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Agata Darmochwal.
Finite sets.
Journal of Formalized Mathematics,
1, 1989.
 [8]
Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski.
Abelian groups, fields and vector spaces.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Andrzej Trybulec.
Domains and their Cartesian products.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [11]
Michal J. Trybulec.
Integers.
Journal of Formalized Mathematics,
2, 1990.
 [12]
Wojciech A. Trybulec.
Vectors in real linear space.
Journal of Formalized Mathematics,
1, 1989.
 [13]
Wojciech A. Trybulec.
Groups.
Journal of Formalized Mathematics,
2, 1990.
 [14]
Wojciech A. Trybulec.
Subgroup and cosets of subgroups.
Journal of Formalized Mathematics,
2, 1990.
 [15]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [16]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received August 10, 1990
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