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Calculus and Beyond Homework Help
What Is the Relationship Between Coset Sizes in a Group?
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[QUOTE="fresh_42, post: 6062391, member: 572553"] I'd say you have ##G= \cup_{(xy)\in G}\,(xy)H##, because there is no need for an external direct product. All ##y\in K## are also in ##G## and so are ##xy \in G##. No need for a separation. Say we have a ##g\in G##, regardless of whether it is ##g=e##.##g=xyh=x'y'h'## I do not see it immediately, since ##x## and ##y## do not commute. IMO there should be some more reasoning, especially as the double usage of ##x## in one and the same equation is a bit weird. See my first remark. The introduction of an artificial external direct product, let it be groups or just sets, is the reason why you are trapped. [/QUOTE]
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What Is the Relationship Between Coset Sizes in a Group?
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