Add to ORKGSummary. In this article, we formalize that every finite cyclic group is isomorphic to a direct product of finite cyclic groups which orders are relative prime. This theorem is closely related to the Chinese Remainder theorem ([18]) and is a useful lemma to prove the basis theorem for finite abelian groups and the fundamental theorem of finite abelian groups. Moreover, we formalize some facts about the product of a finite sequence of abelian groups
Let Γ = {Gi} be a countable collection of groups. Then its cartesian product can be made into a gro...
AbstractA given group G may or may not have the property that there exists a graph X such that the a...
In this article, we formalize that every finite cyclic group is isomorphic to a direct product of fi...
In this article, we formalize that every finite cyclic group is isomorphic to a direct product of fi...
In this paper we formalized some theorems concerning the cyclic groups of prime power order. We form...
Summary.We have been working on the formalization of groups. In [1], we encoded some theorems concer...
Article presenting a direct elementary proof to a classical result regarding the structure of finite...
AbstractHajós theorem asserts that if a finite abelian group is expressed as a direct product of cyc...
Abstract. Direct products of solvable groups in which Sylow-permutability is a transitive relation a...
Given a finite group G, we denote by ? \u27(G) the product of element orders of G. Our main result p...
We determine all the ways in which a direct product of two finite groups can be expressed as the set...
Includes bibliographical references (page 40).Our goal is to count the number of subgroups of the di...
The semidirect product of groups is a generalization of the direct product construction and provides...
Let Γ = {Gi} be a countable collection of groups. Then its cartesian product can be made into a gro...
Let Γ = {Gi} be a countable collection of groups. Then its cartesian product can be made into a gro...
Let Γ = {Gi} be a countable collection of groups. Then its cartesian product can be made into a gro...
AbstractA given group G may or may not have the property that there exists a graph X such that the a...
In this article, we formalize that every finite cyclic group is isomorphic to a direct product of fi...
In this article, we formalize that every finite cyclic group is isomorphic to a direct product of fi...
In this paper we formalized some theorems concerning the cyclic groups of prime power order. We form...
Summary.We have been working on the formalization of groups. In [1], we encoded some theorems concer...
Article presenting a direct elementary proof to a classical result regarding the structure of finite...
AbstractHajós theorem asserts that if a finite abelian group is expressed as a direct product of cyc...
Abstract. Direct products of solvable groups in which Sylow-permutability is a transitive relation a...
Given a finite group G, we denote by ? \u27(G) the product of element orders of G. Our main result p...
We determine all the ways in which a direct product of two finite groups can be expressed as the set...
Includes bibliographical references (page 40).Our goal is to count the number of subgroups of the di...
The semidirect product of groups is a generalization of the direct product construction and provides...
Let Γ = {Gi} be a countable collection of groups. Then its cartesian product can be made into a gro...
Let Γ = {Gi} be a countable collection of groups. Then its cartesian product can be made into a gro...
Let Γ = {Gi} be a countable collection of groups. Then its cartesian product can be made into a gro...
AbstractA given group G may or may not have the property that there exists a graph X such that the a...
In this article, we formalize that every finite cyclic group is isomorphic to a direct product of fi...