Cosets, quotients and homomorphisms 07

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many things are left unstated at 07:30.
For example, why is the observation true?
Why is G a disjoint union over all a \in G (Ans: it is not)
Why is normal subgroup defined with respect to conjugacy, what is significance of conjugacy? (Ans: it is not, it is defined with respect to commutativity)

RahulMadhavan
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