Some topological methods in abstract group theory

1980 ◽  
pp. 86-97
Author(s):  
Alex Heller
Keyword(s):  
Group Theory ◽  
Topological Methods ◽  
Abstract Group

scholarly journals An Overview of the Foundations of the Hypergroup Theory

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1014
Author(s):  
Christos Massouros ◽  
Gerasimos Massouros
Keyword(s):  
Group Theory ◽  
Abstract Algebra ◽  
Special Issue ◽  
Abstract Group ◽  
Structural Relation ◽  
Fundamental Properties ◽  
Theory Versus ◽  
In The Beginning

This paper is written in the framework of the Special Issue of Mathematics entitled “Hypercompositional Algebra and Applications”, and focuses on the presentation of the essential principles of the hypergroup, which is the prominent structure of hypercompositional algebra. In the beginning, it reveals the structural relation between two fundamental entities of abstract algebra, the group and the hypergroup. Next, it presents the several types of hypergroups, which derive from the enrichment of the hypergroup with additional axioms besides the ones it was initially equipped with, along with their fundamental properties. Furthermore, it analyzes and studies the various subhypergroups that can be defined in hypergroups in combination with their ability to decompose the hypergroups into cosets. The exploration of this far-reaching concept highlights the particularity of the hypergroup theory versus the abstract group theory, and demonstrates the different techniques and special tools that must be developed in order to achieve results on hypercompositional algebra.

Topological methods in group theory

1979 ◽  
pp. 137-204 ◽  
Author(s):  
Peter Scott ◽  
Terry Wall
Keyword(s):  
Group Theory ◽  
Topological Methods

The Genesis of the Abstract Group Concept: A Contribution to the History of the Origin of Abstract Group Theory.

1986 ◽  
Vol 93 (10) ◽  
pp. 823
Author(s):  
Karen Hunger Parshall ◽  
Hans Wussing ◽  
Abe Shenitzer
Keyword(s):  
Group Theory ◽  
Abstract Group ◽  
History Of ◽  
Group Concept
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