Concept information
Preferred term
group theory
Definition
-
In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right. Various physical systems, such as crystals and the hydrogen atom, and three of the four known fundamental forces in the universe, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also central to public key cryptography.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Group_theory)
Broader concept
Narrower concepts
- abelian group
- Baum-Connes conjecture
- commutator
- cycle graph
- descendant tree
- finite group
- geometric group theory
- group homomorphism
- idempotent measure
- infinite group
- isomorphism theorem
- Landau's function
- Moufang loop
- nilpotent group
- principal ideal theorem
- quotient group
- simple group
- subgroup
- symmetry group
- topological group
- von Neumann paradox
- Weil conjecture on Tamagawa numbers
In other languages
-
French
URI
http://data.loterre.fr/ark:/67375/PSR-SW10HF3W-P
{{label}}
{{#each values }} {{! loop through ConceptPropertyValue objects }}
{{#if prefLabel }}
{{/if}}
{{/each}}
{{#if notation }}{{ notation }} {{/if}}{{ prefLabel }}
{{#ifDifferentLabelLang lang }} ({{ lang }}){{/ifDifferentLabelLang}}
{{#if vocabName }}
{{ vocabName }}
{{/if}}