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Mathematics LibreTexts

2: Groups

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  • 2.1: Examples of groups
    Groups are one of the most basic algebraic objects, yet have structure rich enough to be widely useful in all branches of mathematics and its applications. A group is a set G with a binary operation G×GG that has a short list of specific properties. Before we give the complete definition of a group in the next section, this section introduces examples of some important and useful groups.
  • 2.2: Definition of a group
    We will use the notation :S×SS to denote a binary operation on a set S that sends the pair (x,y) to xy. Recall that a binary operation is associative means that x(yz)=(xy)z for all x,y,zS.
  • 2.3: Subgroups and Cosets
  • 2.4: Group Homomorphisms
  • 2.5: Group Actions
  • 2.6: Additional exercises


This page titled 2: Groups is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David W. Lyons via source content that was edited to the style and standards of the LibreTexts platform.

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