Beta Phase: Square45 is currently in beta testing. Expect some features or content to be incomplete or missing.

Coset

A set composed of all the products obtained by multiplying each element of a subgroup by a fixed element of the group. Cosets partition the group.

📜

The statement of the theorem

For a subgroup

H \subseteq G

and

g \in G

, the left coset is

gH = \{gh : h \in H\}

and the right coset is

Hg = \{hg : h \in H\}