# Recent questions tagged group-homomorphism

1
A homomorphism $f:G$ to $G1$ of groups is a monomorphism iff Ker $f = \{e\}$.
Verify whether the following mapping is a homomorphism. If so, determine its kernel. $f(x)=x^3$, for all $x$ belonging to $G$.
Verify whether the following mapping is a homomorphism. If so, determine its kernel. $\bar{G}=G$
Verify whether the following mapping is a homomorphism. If so, determine its kernel. $G$ is the group of non zero real numbers under multiplication.