A <group homomorphism> $f:G\to H$ preserves the operation: $f(ab)=f(a)f(b)$ for all $a,b\in G$. A <group isomorphism> is a bijective <group homomorphism>; its inverse also preserves the operation. The <kernel of a group homomorphism> is $\ker f=\{g\in G:f(g)=e_H\}$, a <normal subgroup> of $G$.

Solution

Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2025 / Paper 2 / 9 / a / Solution

 Solution (source code)