Groups

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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