$f: G \to C^{×}$ is homomorphism. |G|=n is abelian .prove that $\sum_{g \in G} f(g)$ is 0 or n
134858
Abelian Group Homomorphism
27728
Question on a homomorphism of a set G.
90332
Prove that that $U(n)$ is an abelian group.
144539
Power series $ f(g(z)) = z $
70298
Are quotients of chain groups $C_n(X)/C_n(A)$ still free?
57809
For which $n$, $G$ is abelian?
40993
Let $f:G\to G'$ be a surjective homomorphism. Prove that if $G$ is cyclic, then $G'$ is cyclic.
90616
When is mapping $g$ to $g^{-1}$ a group homomorphism?
11202
If $g \circ f$ is injective, so is $g$
144105
Ring homomorphism from $\mathbb Z$ to $\mathbb Z$ is always identity or $0$
75315
How to prove that homomorphism from field to ring is injective or zero?
70912
If $g\circ f$ is injective and $f$ is surjective then $g$ is injective
137739
Prove that the group isomorphism $\mathbb{Z}^m \cong \mathbb{Z}^n$ implies that $m = n$
26624
Prove that is group is abelian
157915
Isomorphism between the group $(\mathbb Z[x], +)$ and $(\mathbb Q_{>0}, .)$
153612
Finding $g_i:\mathbb{R}^n\to\mathbb R$ s.t $f(x)=\sum\limits_{i=1}^nx_i\cdot g_i(x)$
130537
Proving that $d(f,g)=\|f-g\| = \sup \limits_{0\leq x \leq 1} |f(x)-g(x)|$ is a metric on $X=C[0,1]$