# Groups -- A Primer

DevFeed: [Groups -- A Primer](<https://devfeed.tech/articles/groups-a-primer-40295.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2012/12/08/groups-a-primer/>)

Published: 2012-12-08T23:42:10Z

Content type: article

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [structure](<https://devfeed.tech/topics/structure.md>), [Math and Logic](<https://devfeed.tech/topics/math-and-logic.md>), [Cryptography](<https://devfeed.tech/topics/cryptography.md>)

Tags: [applications](<https://devfeed.tech/tags/applications.md>), [group-actions](<https://devfeed.tech/tags/group-actions.md>), [groups](<https://devfeed.tech/tags/groups.md>), [lagrange](<https://devfeed.tech/tags/lagrange.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [public-key](<https://devfeed.tech/tags/public-key.md>), [set-theory](<https://devfeed.tech/tags/set-theory.md>), [structure](<https://devfeed.tech/tags/structure.md>), [symmetry](<https://devfeed.tech/tags/symmetry.md>), [theory](<https://devfeed.tech/tags/theory.md>)

## AI overview

This primer introduces group theory as the study of algebraic structures that can describe operations beyond ordinary numbers. It motivates the subject through examples involving symmetry, squares, and Rubik's Cube, and notes applications including public-key cryptography, error detection, crystal structures, particle physics, and mathematical biology.

## Source excerpt

The study of groups is often one's first foray into advanced mathematics. In the naivete of set theory one develops tools for describing basic objects, and through a first run at analysis one develops a certain dexterity for manipulating symbols and definitions. But it is not until the study of groups that one must step back and inspect the larger picture. The main point of that picture (and indeed the main point of a group) is that algebraic structure can be found in the most unalgebraic of settings.