# Search results

1. ### Help Understanding Quotient Groups? (Dummit and Foote)

I don't understand, why can't we just say: If ##aK=a'K## and ##bK=b'K##, then ##(aK)(bK)=(a'K)(bK)=(a'K)(b'K)##. ?
2. ### Help Understanding Quotient Groups? (Dummit and Foote)

I don't see why K needs to be normal? In order for ##(G/K,\cdot)## to be a group we need: i) ##g_1K\cdot(g_2K\cdot{g_3K})=(g_1K\cdot{g_2K})\cdot{g_3K}##. ii) ##\exists{e\in{\frac{G}{K}}}## s.t. for all g in ##\frac{G}{K}##, ##e\cdot{gK}=gK##. iii) for every ##gK\in{\frac{G}{K}}## we need...
3. ### Help Understanding Quotient Groups? (Dummit and Foote)

I left out one part of the definition. It should say "Let ϕ:G→H be a homomorphism with kernel K. The quotient group G/K is the group whose elements are the fibers of ϕ (sets of elements projecting to single elements of H) with group operation defined above: namely if X is the fiber above a...
4. ### Help Understanding Quotient Groups? (Dummit and Foote)

The definition given is... "Let ##\phi: G \rightarrow H## be a homomorphism with kernel ##K##. The quotient group ##G/K## is the group whose elements are the fibers (sets of elements projecting to single elements of H) with group operation defined above: namely if ##X## is the fiber above...