Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
Groups

Wojciech A. Trybulec

Warsaw University
Summary.

Notions of group and abelian group are introduced. The power
of an element of a group, order of group and order of an element of a group
are defined. Basic theorems concerning those notions are presented.
MML Identifier:
GROUP_1
The terminology and notation used in this paper have been
introduced in the following articles
[13]
[6]
[17]
[14]
[18]
[4]
[9]
[5]
[16]
[10]
[15]
[2]
[7]
[12]
[1]
[8]
[3]
[11]
Contents (PDF format)
Bibliography
 [1]
Grzegorz Bancerek.
Cardinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
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.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Czeslaw Bylinski.
Binary operations applied to finite sequences.
Journal of Formalized Mathematics,
2, 1990.
 [8]
Agata Darmochwal.
Finite sets.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Krzysztof Hryniewiecki.
Basic properties of real numbers.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski.
Abelian groups, fields and vector spaces.
Journal of Formalized Mathematics,
1, 1989.
 [11]
Jan Popiolek.
Some properties of functions modul and signum.
Journal of Formalized Mathematics,
1, 1989.
 [12]
Andrzej Trybulec.
Semilattice operations on finite subsets.
Journal of Formalized Mathematics,
1, 1989.
 [13]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [14]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
 [15]
Michal J. Trybulec.
Integers.
Journal of Formalized Mathematics,
2, 1990.
 [16]
Wojciech A. Trybulec.
Vectors in real linear space.
Journal of Formalized Mathematics,
1, 1989.
 [17]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [18]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received July 3, 1990
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