quotient

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introduction

intuition

rigour

Quotient := Let G be a group with H ⊂ G a subgroup.

left_quotien := The quotient $G \diagup H = \{gH|\forall g\in G\}$ is the set of all left cosets.

right_quotien := The quotient H \ G = {Hg|∀g ∈ G} is the set of all right cosets

exam clinic

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examples and non-examples

resources

[[group]] [[set]]

tags :math:

We define a multiplication of two sets A, B as AB = {ab|∀a ∈ A, b ∈ B}

if H ⊲ G then the quotient G \ H equipped with the multiplication law on subsets is a group.

tags: :groups_and_symmetries:

backlinks

• index_of_files.pd