Journal of Formalized Mathematics
Volume 3, 1991
University of Bialystok
Copyright (c) 1991
Association of Mizar Users
Homomorphisms and Isomorphisms of Groups. Quotient Group

Wojciech A. Trybulec

Warsaw University

Michal J. Trybulec

Warsaw University
Summary.

Quotient group, homomorphisms and isomorphisms of groups are introduced.
The so called isomorphism theorems are proved following [9].
MML Identifier:
GROUP_6
The terminology and notation used in this paper have been
introduced in the following articles
[11]
[7]
[19]
[20]
[4]
[6]
[5]
[1]
[8]
[3]
[2]
[12]
[13]
[10]
[15]
[17]
[14]
[16]
[18]
Contents (PDF format)
Bibliography
 [1]
Grzegorz Bancerek.
Cardinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Jozef Bialas.
Group and field definitions.
Journal of Formalized Mathematics,
1, 1989.
 [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.
Partial functions.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [8]
Agata Darmochwal.
Finite sets.
Journal of Formalized Mathematics,
1, 1989.
 [9]
M. I. Kargapolow and J. I. Mierzlakow.
\em Podstawy teorii grup.
PWN, War\sza\wa, 1989.
 [10]
Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski.
Abelian groups, fields and vector spaces.
Journal of Formalized Mathematics,
1, 1989.
 [11]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [12]
Michal J. Trybulec.
Integers.
Journal of Formalized Mathematics,
2, 1990.
 [13]
Wojciech A. Trybulec.
Vectors in real linear space.
Journal of Formalized Mathematics,
1, 1989.
 [14]
Wojciech A. Trybulec.
Classes of conjugation. Normal subgroups.
Journal of Formalized Mathematics,
2, 1990.
 [15]
Wojciech A. Trybulec.
Groups.
Journal of Formalized Mathematics,
2, 1990.
 [16]
Wojciech A. Trybulec.
Lattice of subgroups of a group. Frattini subgroup.
Journal of Formalized Mathematics,
2, 1990.
 [17]
Wojciech A. Trybulec.
Subgroup and cosets of subgroups.
Journal of Formalized Mathematics,
2, 1990.
 [18]
Wojciech A. Trybulec.
Commutator and center of a group.
Journal of Formalized Mathematics,
3, 1991.
 [19]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [20]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received October 3, 1991
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