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2: Introduction to Groups

  • Page ID
    97985
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    One of the major topics of this course is groups. The area of mathematics that is concerned with groups is called group theory. Loosely speaking, group theory is the study of symmetry, and in my opinion is one of the most beautiful areas in all of mathematics. It arises in puzzles, visual arts, music, nature, the physical and life sciences, computer science, cryptography, and of course, throughout mathematics.

    • 2.1: A First Example
    • 2.2: Binary Operation
      Before beginning our formal study of groups, we need to have an understanding of binary operations. After learning to count as a child, you likely learned how to add, subtract, multiply, and divide with real numbers. As long as we avoid division by zero, these operations are examples of binary operations since we are combining two objects to obtain a single object.
    • 2.3: Groups
    • 2.4: Generating Sets
    • 2.5: Group Tables
      Recall that we could represent a binary operation on a finite set using a table. Since groups have binary operations at their core, we can represent a finite group (i.e., a group with finitely many elements) using a table, called a group table.
    • 2.6: Cayley Diagrams
      In this section, we will introduce visual way of encoding the abstract structure of the group in terms of a specified generating set. To get started, let’s tinker with an example.


    This page titled 2: Introduction to Groups is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Dana Ernst via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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