A Quick Review of Group Theory: Homomorphisms, Quotient Groups, Representations, and Extensions

One of the simplest and most widely used mathematical concepts in physics is the concept of a group. Group theory is central to the study of symmetry. This article reviews some basic definitions in group theory.

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Revision history

2024-05-21 (changed the title to be more descriptive)
2024-04-01 (added a footnote about terminology)
2024-03-04 (updated publication info for one reference)
2024-02-25 (added another example of isomorphism)
2022-06-11 (updated references to other articles in this series to link to html abstract pages instead of to pdfs. Didn't change the version number/date)
2022-02-18 (added more references)
2022-02-07 (first version)

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updated 2025-06-29

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A Quick Review of Group Theory: Homomorphisms, Quotient Groups, Representations, and Extensions

Revision history