Quotient group

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created: 2021-12-06 13:20:31
modified: 2022-01-10 04:13:04

is a group and .
Then is also a group with the set product "".

Proof that it is indeed a group

We need to check the group axioms:

0. Is it closed?

Is the product of two cosets is always a coset?

1. Is it associative?

Easy to see that it is true.

2. Neutral element?

3. Inverse of ?