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.III-24.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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