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In summary, the conversation discusses a homomorphism and its kernel, and how to enumerate all of the cosets of the kernel. The speaker suggests using an epimorphism to find a subset of elements that can generate all cosets when multiplied by the kernel. Additionally, the speaker notes that the groups involved are only additive.

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I see only additive groups here, so it has to be ##g+\operatorname{ker}(\pi)##. Moreover we have an epimorphism, so we get an induced isomorphism ##\bar{\pi}\, : \,\mathbb{R} \cong \mathbb{R}^2/\operatorname{ker}(\pi)## which means, all elements are of the form ##g+\mathbb{R}## where ##\mathbb{R}=\operatorname{ker}(\pi)## is the diagonal, which is shifted upwards (##g>0##) or downwards (##g<0##) to cover the entire plane by copies of said diagonal.Mr Davis 97 said:

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