How to show that $\phi(g)=g^{-1}$ is a group homomorphism iff $G$ is abelian?
73988
Characterize the groups $G$ for which the map $\iota: G \to G$, sending $x \mapsto x^{-1}$ for all $x \in G$, is an automorphism of $G$
23279
Group Theory Isomorphism
44258
Conditions under which group solvability is invariant under an homomorphism.
26624
Prove that is group is abelian
139100
A question on the group algebra $k[G]$ of a finite abelian group
29717
Not sure how to go about this group theory proof
41237
$H$ is normal subgroup of $G$ iff $gHg^{-1}=H$ for every $g$ of $G$
23579
If $G$ is isomorphic to $H$, then ${\rm Aut}(G)$ is isomorphic to ${\rm Aut}(H)$
112993
Is every quotient of a finite abelian group $G$ isomorphic to some subgroup of $G$?
60208
Proof of property of abelian group
32428
Group homomorphisms and which of the following statements are true (NBHM-$2014$)
130081
Show that $A_n$ is the kernel of a group homomorphism of $S_n \rightarrow \{−1,1\}$.
126930
Finding all group homomorphisms of $S_n\to\mathbb{C}^*$ and $A_n\to\mathbb{C}^*$
136083
Show that $\sigma\circ\phi : G_1 \to G_3$ is an isomorphism
65900
Show that a finite group with certain automorphism is abelian
1364
Let $G$ be a group in which $a^2=e$ for all elements of $a$ of $G$. Show that $G$ is Abelian.
27728
Question on a homomorphism of a set G.