Talk:Coset Product is Well-Defined

Coset product should be distinguished from subset product by separate notation (at the moment both are denoted with $\circ$) because this result is established by Coset Product Consistent with Subset Product Definition. I'd propose to denote first with $\circ$ and second by juxtaposition; other propositions are warmly welcome! (maybe $\circ$ and $\bullet$ respectively!?) BTW. In some places cosets are denoted like $aH$ and in some places like $a \circ H$, this is little bit inconsistent… joel talk 18:15, 29 December 2012 (UTC)


 * What's wrong with mentioning that the same notation is used, with reference to the result that they are compatible? --Lord_Farin (talk) 18:59, 29 December 2012 (UTC)


 * I think it won't be as clear as with above distinction: in coset space you can introduce many different operations, coset product is one of them. But please notice that subset product (complex product) is defined for any non-empty subgroup subset (which is called a complex) and as such is more general. It just happens that if one restricts himself to complexes which are (left/right) cosets then the result of their complex product is also (the same kind of) coset. Only then those operations coincide. joel talk 19:25, 29 December 2012 (UTC) P.S. Coset product is well-defined iff factor subgroup is normal; subgroup product is always well-defined—this also shows that those are different.


 * There is no difference between coset product and subset product but that the former is of an element and the latter is a set. The distinction is mentioned in one of the pages but it's so trivial it's barely even worth discussing. I see no reason to change our approach. --prime mover (talk) 21:37, 29 December 2012 (UTC)