$\textbf{Kernel of a group homomorphism}$
Let $\varphi:G\to H$ be a homomorphism between two groups $G$ and $H$. The kernel of $\varphi$ is the set of all elements of $G$ which are mapped to the neutral element $e\in H$, i.e. $\{{g\in G:\varphi(g)=e\}}$.
Note: The kernel of $\varphi$ is a subgroup of $G$.
$\textbf{Kernel of a group homomorphism}$
Let $\varphi:G\to H$ be a homomorphism between two groups $G$ and $H$. The kernel of $\varphi$ is the set of all elements of $G$ which are mapped to the neutral element $e\in H$, i.e. $\{{g\in G:\varphi(g)=e\}}$.
Note: The kernel of $\varphi$ is a subgroup of $G$.
copied
𝐊𝐞𝐫𝐧𝐞𝐥 𝐨𝐟 𝐚 𝐠𝐫𝐨𝐮𝐩 𝐡𝐨𝐦𝐨𝐦𝐨𝐫𝐩𝐡𝐢𝐬𝐦
Let 𝜑:𝐺→𝐻 be a homomorphism between two groups 𝐺 and 𝐻. The kernel of 𝜑 is the set of all elements of 𝐺 which are mapped to the neutral element 𝑒∈𝐻, i.e. {𝑔∈𝐺:𝜑(𝑔)=𝑒}.
Note: The kernel of 𝜑 is a subgroup of 𝐺.