If $f:G \rightarrow G$ is a group homomorphism and $f(ab) = f(b)f(a)$ does this show that $f$ is NOT a homomorphism?
25439
f(a) = inverse of a is an isomorphism iff a group G is Abelian
25050
To prove that $(F,+)$ and $(F-\{0\},\cdot)$ are not isomorphic as groups.
120971
(Revised) Prove that $\phi$ is a group homomorphism and find the kernel.
152603
Group isomorphic to its automorphism group
28252
How many homomorphisms are there from $\Bbb Z_{20}$ onto $\Bbb Z_{8}$? How many are there to $\Bbb Z_{8}$?
132704
If G is not commutative, then is there always a subgroup that is not a normal subgroup?
148616
When is a ring homomorphism $A \to A$ surjective but not injective.
154847
homomorphism from $S_3$ to $\mathbb Z/3\mathbb Z$
46342
Prove that $G$ is abelian iff $\varphi(g) = g^2$ is a homomorphism
58766
free groups: $F_X\cong F_Y\Rightarrow|X|=|Y|$
158282
Finite order of an element $f(g)$ of a homomorphism $f$
129452
Groups $G,H$ with surjective homomorphisms that are quotient of each other
153291
Why a ring homomorphism from a local ring will not map a non-unit to a unit？
123419
Abstract algebra: homomorphism and an element of a prime order
119648
For which $n$ and $k$ are there nontrivial homomorphisms from $S_n$ to $\mathbb{Z}/k\mathbb{Z}$?
126930
Finding all group homomorphisms of $S_n\to\mathbb{C}^*$ and $A_n\to\mathbb{C}^*$
32127
Example where $f\circ g$ is bijective, but neither $f$ nor $g$ is bijective