Math and science::Algebra::Aluffi

Cosets

Let $G$ be a group and $H \subset G$ a subgroup.

For any $a \in G$ , a right-coset of $H$ is any set of the form:

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?

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For any $a \in G,$ a left-coset of $H$ is any set of the form:

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?

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A right-coset forms a block in a partition defined by an equivalence relation, $\sim_{R}$ .

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x \sim_{R} y ⟺ ?

]

A left-coset forms a block in a partition defined by a equivalence relation, $\sim_{L}$ .

[

x \sim_{L} y ⟺ ?

]

The essence of the relations is to consider an element related to another if the inverse of one element brings the other element back to $H$ .

03.04.2022