In mathematics and 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, 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.
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This is a listof number theorytopics. See also: Listof recreational number theorytopicsTopics in cryptography Composite number Highly composite number...
a listof mathematical topics in quantum theory, by Wikipedia page. See also listof functional analysis topics, listof Lie grouptopics, listof quantum-mechanical...
This is a listof string theorytopics. Strings Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string...
This is a listof algebraic number theorytopics. These topics are basic to the field, either as prototypical examples, or as basic objects of study. Algebraic...
In abstract algebra, grouptheory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known...
or "precedes" another. An alphabetical listof many notions of order theory can be found in the order theory glossary. See also inequality, extreme value...
This is a listof Lie grouptopics, by Wikipedia page. See Table of Lie groups for a list General linear group, special linear group SL2(R) SL2(C) Unitary...
This is a listof representation theorytopics, by Wikipedia page. See also listof harmonic analysis topics, which is more directed towards the mathematical...
Knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs...
topics for more theoryof algorithms. Peano axioms Giuseppe Peano Mathematical induction Structural induction Recursive definition Naive set theory Element...
outline is provided as an overview of and topical guide to critical theory: Critical theory – the examination and critique of society and culture, drawing from...
a listoftopics that have, either currently or in the past, been characterized as pseudoscience by academics or researchers. Detailed discussion of these...
This is a listof integration and measure theorytopics, by Wikipedia page. Length Area Volume Probability Moving average Riemann sum Riemann–Stieltjes...
specifically grouptheory, a nilpotent group G is a group that has an upper central series that terminates with G. Equivalently, it has a central series of finite...
important to diverse areas of mathematics such as Galois theory, invariant theory, the representation theoryof Lie groups, and combinatorics. Cayley's...
Adjoint representation of a Lie group Haar measure Homogeneous space Listof Lie grouptopics Representations of Lie groups Symmetry in quantum mechanics...
specifically in the field ofgrouptheory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions. Equivalently...
aspects of the theoryof finite groups in great depth, especially the local theoryof finite groups and the theoryof solvable and nilpotent groups. As a...
permutation groups is Burnside's TheoryofGroupsof Finite Order of 1911. The first half of the twentieth century was a fallow period in the study ofgroup theory...
groups (the automorphism group GL(V) is a linear group but not a matrix group). These groups are important in the theoryofgroup representations, and also...
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