Group theory/Related Articles

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A list of Citizendium articles, and planned articles, about Group theory.
See also changes related to Group theory, or pages that link to Group theory or to this page or whose text contains "Group theory".

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  • Abstract algebra [r]: Branch of mathematics that studies structures such as groups, rings, and fields. [e]
  • Algebra [r]: A branch of mathematics concerning the study of structure, relation and quantity. [e]
  • Angular momentum (classical) [r]: The tendency of a rotating object to resist changes to its rotational motion. [e]
  • Angular momentum (quantum) [r]: A vector operator of which the three components have well-defined commutation relations. [e]
  • Automorphism [r]: An isomorphism of an algebraic structure with itself: a permutation of the underlying set which respects all algebraic operations. [e]
  • Baer-Specker group [r]: An example of an infinite Abelian group which is a building block in the structure theory of such groups. [e]
  • Centraliser [r]: The set of all group elements which commute with every element of a given subset. [e]
  • Centre of a group [r]: The subgroup of a group consisting of all elements which commute with every element of the group. [e]
  • Character (group theory) [r]: A homomorphism from a group to the unit circle; more generally, the trace of a group representation. [e]
  • Characteristic subgroup [r]: A subgroup which is mapped to itself by any automorphism of the whole group. [e]
  • Commutator [r]: A measure of how close two elements of a group are to commuting. [e]
  • Composition (mathematics) [r]: Add brief definition or description
  • Conjugacy [r]: In group theory, this describes the relation between elements of a group that states that one element is the conjugate of the other. [e]
  • Conjugation (group theory) [r]: The elements of any group that may be partitioned into conjugacy classes. [e]
  • Cyclic group [r]: A group consisting of the powers of a single element. [e]
  • Edward Teller [r]: (January 15, 1908 - September 9, 2003) One of the most controversial scientists of the 20th century because of his role as the main developer of the hydrogen bomb, his outspoken defense of an unassailable nuclear arsenal, and support for President Reagan's Strategic Defensive Initiative. [e]
  • Exact sequence [r]: A sequence of algebraic objects and morphisms which is used to describe or analyse algebraic structure. [e]
  • Examples of groups [r]: Add brief definition or description
  • Frattini subgroup [r]: The intersection of all maximal subgroups of a group. [e]
  • Free group [r]: A group in which there is a generating set such that every element of the group can be written uniquely as the product of generators. [e]
  • Galois theory [r]: Algebra concerned with the relation between solutions of a polynomial equation and the fields containing those solutions. [e]
  • Gaussian type orbitals [r]: Functions used as atomic orbitals in the LCAO method for the computation of electron orbitals in molecules. [e]
  • Group (mathematics) [r]: Set with a binary associative operation such that the operation admits an identity element and each element of the set has an inverse element for the operation. [e]
  • Group action [r]: A way of describing symmetries of objects using groups. [e]
  • Group homomorphism [r]: A map between group which preserves the group structure. [e]
  • Integer [r]: The positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero. [e]
  • Mathematics [r]: The study of quantities, structures, their relations, and changes thereof. [e]
  • Normaliser [r]: The elements of a group which map a given subgroup to itself by conjugation. [e]
  • Number theory [r]: The study of integers and relations between them. [e]
  • Order (group theory) [r]: For a group, its cardinality; for an element of a group, the least positive integer (if one exists) such that raising the element to that power gives the identity. [e]
  • Permutation group [r]: Group whose elements are permutations of some set of symbols where the product of two permutations is the permutation arising from successive application of the two. [e]
  • Residual property (mathematics) [r]: A concept in group theory on recovered element properties. [e]
  • Ring (mathematics) [r]: Algebraic structure with two operations, combining an abelian group with a monoid. [e]
  • Serge Lang [r]: (19 May 1927 – 12 September 2005) French-born American mathematician known for his work in number theory and for his mathematics textbooks, including the influential Algebra. [e]
  • Series (group theory) [r]: A chain of subgroups of a group linearly ordered by subset inclusion. [e]
  • Subgroup [r]: A subset of a group which is itself a group with respect to the group operations. [e]
  • Sylow subgroup [r]: A subgroup of a finite group whose order is the largest possible power of one of the primes factors of the group order. [e]
  • Symmetric group [r]: The group of all permutations of a set, that is, of all invertible maps from a set to itself. [e]
  • World War II, air war, Mediterranean and European tactical operations [r]: Following the cancellation of the invasion of Britain, while harassment continued of the British Isles and the Eastern Front, the Germans searched for new opportunities in 1940-1941, finding them in Southern Europe, met, in part, by the invasion of North Africa in 1942, which led to the Italian campaign. [e]