Artin–Tits group & Group (mathematics) - Unionpedia, the concept map

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Difference between Artin–Tits group and Group (mathematics)

Artin–Tits group vs. Group (mathematics)

In the mathematical area of group theory, Artin groups, also known as Artin–Tits groups or generalized braid groups, are a family of infinite discrete groups defined by simple presentations. In mathematics, a group is a set with an operation that associates an element of the set to every pair of elements of the set (as does every binary operation) and satisfies the following constraints: the operation is associative, it has an identity element, and every element of the set has an inverse element.

Free group

In mathematics, the free group FS over a given set S consists of all words that can be built from members of S, considering two words to be different unless their equality follows from the group axioms (e.g. st.

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Fundamental group

In the mathematical field of algebraic topology, the fundamental group of a topological space is the group of the equivalence classes under homotopy of the loops contained in the space.

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Graph (discrete mathematics)

In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense "related".

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Group (mathematics)

In mathematics, a group is a set with an operation that associates an element of the set to every pair of elements of the set (as does every binary operation) and satisfies the following constraints: the operation is associative, it has an identity element, and every element of the set has an inverse element.

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Group cohomology

In mathematics (more specifically, in homological algebra), group cohomology is a set of mathematical tools used to study groups using cohomology theory, a technique from algebraic topology.

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Group theory

In abstract algebra, group theory studies the algebraic structures known as groups.

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Jacques Tits

Jacques Tits (12 August 1930 – 5 December 2021) was a Belgian-born French mathematician who worked on group theory and incidence geometry.

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Mathematische Annalen

Mathematische Annalen (abbreviated as Math. Ann. or, formerly, Math. Annal.) is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann.

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Monoid

In abstract algebra, a branch of mathematics, a monoid is a set equipped with an associative binary operation and an identity element.

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Presentation of a group

In mathematics, a presentation is one method of specifying a group.

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Torsion (algebra)

In mathematics, specifically in ring theory, a torsion element is an element of a module that yields zero when multiplied by some non-zero-divisor of the ring.

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