I read the following definition: $G/H$ is the set of left cosets of $G$ modulo $H$ (Where $G$ and $H$ are groups).
Now, what I don't understand is: what does $G$ modulo $H$ mean?
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1Refers to the same thing. – AJY Feb 21 '17 at 15:14
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1Have a look at this answer http://math.stackexchange.com/a/1733675/285940 – Edu Feb 21 '17 at 15:16
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A quotient $G/H$ is the original set $G$ partitioned by an equivalence relation defined by the group $H$. That is: we says that $$p\sim q\iff p\in q\odot H$$ for all $p,q\in G$, where $\odot$ is the group operation in $G$. – Masacroso Feb 21 '17 at 16:13
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See also here. – Jyrki Lahtonen Sep 13 '19 at 16:05
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It means the group of elements of $G$ collected together by whether they differ by an element of $H$; in effect, it generalises the notion of integers modulo some number $n$, since, in that case, one considers the integers in equivalence classes according to how they differ by a multiple of $n$.
Shaun
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