Explore the concept of cosets within groups, defined as the set of all possible products between elements of a subgroup and the group's elements. Learn about right and left cosets, congruence modulo a subgroup, and the properties of equivalence relations within group theory. Dive into examples and t

3 views • 10 slides

Explore the concept of cosets in group theory, with a focus on right cosets, left cosets, and congruence modulo a subgroup. Learn how to determine cosets, understand the relation between elements in a group, and establish equivalence relations through examples and definitions.

0 views • 10 slides

In group theory, a subgroup H of a group G helps decompose G into equal-size disjoint subsets called cosets. Quotient spaces in mathematics involve equivalence classes under a given relation and a specific topology. Furthermore, in linear algebra, the quotient of a vector space by a subspace results

0 views • 8 slides