Group theory - Revision history

Karl Jones: /* External links */

2016-04-17T21:09:59Z

‎External links

Karl Jones at 21:09, 17 April 2016

2016-04-17T21:09:18Z

Karl Jones: /* See also */

2016-02-20T12:23:25Z

‎See also

Karl Jones: Created page with "In mathematics and abstract algebra, '''group theory''' studies the algebraic structures known as groups. == Description == The concept of a group is central to ab..."

2016-02-18T03:01:33Z

Created page with "In mathematics and abstract algebra, '''group theory''' studies the algebraic structures known as groups. == Description == The concept of a group is central to ab..."

New page

In [[mathematics]] and [[abstract algebra]], '''group theory''' studies the algebraic structures known as groups.

== Description ==

The concept of a group is central to [[abstract algebra]].

Various well-known algebraic structures, such as [[Ring (mathematics)|rings]], [[Field (mathematics)|fields]], and [[Vector space|vector spaces]], can all be seen as groups endowed with additional [[Operation (mathematics)|operations]] and [[Axiom|axioms]].

== Influence ==

Groups recur throughout [[mathematics]], and the methods of group theory have influenced many parts of [[algebra]].

== Branches ==

[[Linear algebraic group|Linear algebraic groups]] and [[Lie group|Lie groups]] are two branches of group theory that have experienced advances and have become subject areas in their own right.

== Physical systems and applications ==

Various physical systems, such as [[Crystal|crystals]] and the hydrogen atom, may be modelled by [[Symmetry group|symmetry groups]].

Thus group theory and the closely related [[representation theory]] have many important applications in [[physics]], [[chemistry]], and [[materials science]].

== Public key cryptography ==

Group theory is central to [[public key cryptography]].

== Finite simple groups ==

One of the most important mathematical achievements of the 20th century was the collaborative effort, taking up more than 10,000 journal pages and mostly published between 1960 and 1980, that culminated in a complete classification of [[Finite simple group|finite simple groups]].

== See also ==

* [[Abstract algebra]]
* [[Finite simple group]]
* [[Mathematics]]
* [[Public key cryptography]]

== External links ==

* [https://en.wikipedia.org/wiki/Group_theory Group theory] @ Wikipedia

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 * [https://en.wikipedia.org/wiki/Group_theory Group theory] @ Wikipedia
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 [[Category:Mathematics]]

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	* [https://en.wikipedia.org/wiki/Group_theory Group theory] @ Wikipedia		* [https://en.wikipedia.org/wiki/Group_theory Group theory] @ Wikipedia
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 * [[Abstract algebra]]
 * [[Finite simple group]]
 * [[Mathematics]]
 * [[Public key cryptography]]