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| Title Details: | |
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Groups |
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| Authors: |
Papistas, Athanasios |
| Reviewer: |
Metaftsis, Vasileios |
| Description: | |
| Abstract: |
As a natural preliminary to the concept of a group, the notion of a semigroup is introduced, and its basic properties are studied. We define equivalence relations on a non-empty set and the corresponding quotient set. Some fundamental concepts from elementary Number Theory are also developed, as they play a significant role in Group Theory—such as prime numbers, Euclidean division, congruences, and primitive roots—from which examples of groups are drawn. We then study permutations (on a finite set) and their key properties. Exercises are provided.
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| Type: |
Chapter |
| Creation Date: | 2015 |
| Item Details: | |
| License: |
http://creativecommons.org/licenses/by-nc-nd/3.0/gr |
| Handle | http://hdl.handle.net/11419/1172 |
| Bibliographic Reference: | Papistas, A. (2015). Groups [Chapter]. In Papistas, A. 2015. Group Theory Lessons [Undergraduate textbook]. Kallipos, Open Academic Editions. https://hdl.handle.net/11419/1172 |
| Language: |
Greek |
| Is Part of: |
Group Theory Lessons |
| Number of pages |
31 |
| Publication Origin: |
Kallipos, Open Academic Editions |