Concept

Green's relations

Related lectures (8)

Quotients of Groups by Relations of Equivalence

Explores quotients of groups by equivalence relations and the conditions for well-defined sets.

Explores Lagrange's theorem in commutative groups and the concept of equivalence relations, demonstrating their practical applications.

Number Theory: Operations and Equivalence

Covers operations and equivalence relations in number theory, including addition, subtraction, multiplication, division, and properties of neutral and inverse elements.

Group Theory: Part 2

Delves into advanced group theory concepts such as isomorphisms and homomorphisms.

Groupes Isomorphes: Applications

Explores isomorphic groups, bijective morphisms, and their applications in group theory.

Subgroups and Cosets: Lagrange's Theorem

Explores subgroups, normal subgroups, cosets, and Lagrange's theorem in group theory, emphasizing the importance of left cosets.

Relations and Sequences: Well-ordered Sets and Geometric Series

Explores equivalence relations, well-ordered sets, geometric series, and countable sets.

Motivations for studying group actions

Covers group actions, bijections, evaluations, translations, homomorphisms, and inverses within universal actions.