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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.
Generalized orthogonal group, generalized special orthogonal group. The special unitary group SU(1,1) is the unit sphere in the ring of coquaternions. It is the group of hyperbolic motions of the Poincaré disk model of the Hyperbolic plane. Lorentz group; Spinor group; Symplectic group; Exceptional groups G 2; F 4; E 6; E 7; E 8; Affine group ...
Group theory has three main historical sources: number theory, the theory of algebraic equations, and geometry.The number-theoretic strand was begun by Leonhard Euler, and developed by Gauss's work on modular arithmetic and additive and multiplicative groups related to quadratic fields.
The group consists of the finite strings (words) that can be composed by elements from A, together with other elements that are necessary to form a group. Multiplication of strings is defined by concatenation, for instance (abb) • (bca) = abbbca. Every group (G, •) is basically a factor group of a free group generated by G.
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Fibonacci group; List of finite simple groups; List of spherical symmetry groups; Finite subgroups of SU(2) Finitely generated group; Finiteness properties of groups; Fixed points of isometry groups in Euclidean space; Formation (group theory) Frattini subgroup; Free partially commutative group