study of algebraic groups belongs both to algebraic geometry and group theory. Many groups of geometric transformations are algebraic groups; for example...

In abstract algebra, an adelic algebraic group is a semitopological group defined by an algebraic group G over a number field K, and the adele ring A...

special orthogonal group SO(n), and the symplectic group Sp(2n). Simple algebraic groups and (more generally) semisimple algebraic groups are reductive. Claude...

defined by polynomials, that is, that these are algebraic groups. The founders of the theory of algebraic groups include Maurer, Chevalley, and Kolchin (1948)...

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...

of an algebraic group is the identity component of its maximal normal solvable subgroup. For example, the radical of the general linear group GL n ⁡...

the unitary group is a linear algebraic group. The unitary group of a quadratic module is a generalisation of the linear algebraic group U just defined...

equals its transpose). The orthogonal group is an algebraic group and a Lie group. It is compact. The orthogonal group in dimension n has two connected components...

abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures...

Zhenheng Li; Benjamin Steinberg; Qiang Wang (2014). Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics. Springer. p. 142. ISBN 978-1-4939-0938-4...