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## Main Question or Discussion Point

Outside of pure mathematics, where is group theory used?

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Outside of pure mathematics, where is group theory used?

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HallsofIvy

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Also group theory can be used to determine which polynomial equations can be solved in terms of radicals. (That was, in fact, the main reason for the development of group theory.) That is still mathematics but not what I would consider "pure" mathematics.

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Group theory is extensively applied in Theoretical Physics:

General and Spacial Relativity

Elementary Particles

Quantum Physics

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http://www.google.com/search?sourceid=chrome&ie=UTF-8&q=rubik's+cube+group+theory

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Deveno

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group theory is an important part of cryptography (the study of codes), and plays a prominent role in understanding such techniques as RSA encryption.

cyclic groups play a role in musicology, and form a mathematical basis for the 12-tone system.

group theory is important in algebraic topology, which finds application, among other things, in design of computer networks and communication systems.

finally, there is group theory in symmetric artistic design elements (the so-called "frieze groups" and "ornament groups") used in textiles, printing, wall-papers, tiling (especially in arabic mosques), and such common-place items as kaleidoscopes (reflections form a group).

in short, groups are everywhere! if you've ever "counted by 2's or 3's" you were using intuitively a natural group property of the integers. the shuffling of a deck of cards, rotating a sphere in space, even our way of using a circle to measure time, these are all groups at work in our everyday lives.

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mathwonk

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group theory is the mathematics of symmetry, so just think about the places where symmetry occurs.

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