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Cyclic soft groups and their applications on groups
1Department of Mathematics, Faculty of Science, Erciyes University, 38039 Kayseri, Turkey ; Department of Mathematics, Faculty of Science, Erciyes University, 38039 Kayseri, Turkey.
This study introduces novel concepts for soft groups, including their order, power, and cyclic properties. It explores the connections between these soft group structures and traditional group theory.
Area of Science:
- Abstract algebra
- Fuzzy set theory
Background:
- The concepts of group order and cyclic groups are fundamental in abstract algebra.
- Applications of these classical group notions are widespread.
Purpose of the Study:
- To introduce and define the order of soft groups.
- To define and investigate the power of soft sets and soft groups.
- To introduce the concept of cyclic soft groups and analyze their relationship with classical groups.
Main Methods:
- Extension of classical group theory concepts to the framework of soft sets.
- Development of definitions for order, power, and cyclic properties within soft groups.
- Comparative analysis between soft group properties and their classical counterparts.
Main Results:
- Definitions for order of soft groups, power of soft sets, power of soft groups, and cyclic soft groups are established.
- The interrelationships between these newly defined soft group concepts are explored.
- The relationship between cyclic soft groups and classical groups is investigated.
Conclusions:
- The paper successfully extends classical group theory concepts to soft groups.
- New theoretical frameworks for soft group analysis are provided.
- The findings contribute to a deeper understanding of algebraic structures in soft set theory.
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