Volume 4, 1992

University of Bialystok

Copyright (c) 1992 Association of Mizar Users

**Dariusz Surowik**- Warsaw University, Bialystok

- Some theorems and properties of cyclic groups have been proved with special regard to isomorphisms of these groups. Among other things it has been proved that an arbitrary cyclic group is isomorphic with groups of integers with addition or group of integers with addition modulo $m$. Moreover, it has been proved that two arbitrary cyclic groups of the same order are isomorphic and that the class of cyclic groups is closed in consideration of homomorphism images. Some other properties of groups of this type have been proved too.

Contents (PDF format)

- [1]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [2]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
*Journal of Formalized Mathematics*, 1, 1989. - [3]
Czeslaw Bylinski.
Functions and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [4]
Czeslaw Bylinski.
Functions from a set to a set.
*Journal of Formalized Mathematics*, 1, 1989. - [5]
Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski.
Abelian groups, fields and vector spaces.
*Journal of Formalized Mathematics*, 1, 1989. - [6]
Rafal Kwiatek and Grzegorz Zwara.
The divisibility of integers and integer relatively primes.
*Journal of Formalized Mathematics*, 2, 1990. - [7]
Dariusz Surowik.
Cyclic groups and some of their properties --- part I.
*Journal of Formalized Mathematics*, 3, 1991. - [8]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [9]
Michal J. Trybulec.
Integers.
*Journal of Formalized Mathematics*, 2, 1990. - [10]
Wojciech A. Trybulec.
Vectors in real linear space.
*Journal of Formalized Mathematics*, 1, 1989. - [11]
Wojciech A. Trybulec.
Classes of conjugation. Normal subgroups.
*Journal of Formalized Mathematics*, 2, 1990. - [12]
Wojciech A. Trybulec.
Groups.
*Journal of Formalized Mathematics*, 2, 1990. - [13]
Wojciech A. Trybulec.
Lattice of subgroups of a group. Frattini subgroup.
*Journal of Formalized Mathematics*, 2, 1990. - [14]
Wojciech A. Trybulec.
Subgroup and cosets of subgroups.
*Journal of Formalized Mathematics*, 2, 1990. - [15]
Wojciech A. Trybulec and Michal J. Trybulec.
Homomorphisms and isomorphisms of groups. Quotient group.
*Journal of Formalized Mathematics*, 3, 1991. - [16]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [17]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989.

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