If $G$ is a group and $f: G \to G$ is defined by $f(x) = x^{-1}$ is it a homomorphism?
90616
When is mapping $g$ to $g^{-1}$ a group homomorphism?
88928
$F:G\to B$ is an isomorphism between groups implies $F^{-1}$ is an isomorphism
112993
Is every quotient of a finite abelian group $G$ isomorphic to some subgroup of $G$?
90192
Kernel and Image of a group homomorphism
120971
(Revised) Prove that $\phi$ is a group homomorphism and find the kernel.
32428
Group homomorphisms and which of the following statements are true (NBHM-$2014$)
116168
Is $e^x$ the only isomorphism between the groups $(\mathbb{R},+)$ and $(\mathbb{R}_{> 0},*)$?
103801
$xT=x$ iff $x=e$ implies that every $g$ may be written as $x^{-1}(xT)$ for some $x\in G$.
27728
Question on a homomorphism of a set G.
153797
Is a quotient group a subgroup?
40069
The image of a homomorphism is a group?
51145
Is it possible to prove $g^{|G|}=e$ in all finite groups without talking about cosets?
642
Does a surjective ring homomorphism have to be surjective on the unit groups?
146952
When can I say that $\cup H_i$ is a group?
55976
Are groups satisfying $g=g^{-1}$ for all $g \in G$ abelian?
120495
Does this correctly interpret the "$\cong$" between groups as "$=$" between sets?
150585
Group with $a=a^{-1}$ for all $a\in G$ is abelian