New posts in normal-subgroups

How to show that Klein four-group is a normal subgroup of the alternating group $A_4$

Understanding a proof of: If $N\unlhd G$ s.t. $N$ and $G/N$ are solvable, then $G$ is solvable.

If $H,K⊲G$ and $H∩K = \{1_G\}$, then all elements in $H$ commute with all elements in $K$ [duplicate]

Some Subgroup of Dihedral Group is Normal

Intersection of conjugate subgroups is normal

Let $H$ be a subgroup of a group $G$ such that $x^2 \in H$ , $\forall x\in G$ . Prove that $H$ is a normal subgroup of $G$

Are there any natural numbers $n$ that satisfy the condition $7921\sigma(n) = 15840n$?

Prove that the center of a group is a normal subgroup [closed]

Inner automorphisms form a normal subgroup of $\operatorname{Aut}(G)$

If $N$ is a normal subgroup of $G$, show $Z(G)N/N \subset Z(G/N)$ [closed]

All $p$-groups have a normal subgroup of each possible order. [duplicate]

Prove that: A group $G$ of order $p^n$ has normal subgroup of order $p^k$, for all $0\le k\le n$.

If $N$ is normal in $G$, show $Z_{i}(G)N/N \leq Z_{i}(G/N)$ where $Z_{i}(G)$ is the $i$th term in the upper central series for $G$.

If $H$ is a cyclic subgroup of $G$ and $H$ is normal in $G$, then every subgoup of $H$ is normal in $G$.

Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$

A Group Having a Cyclic Sylow 2-Subgroup Has a Normal Subgroup.

Intuition behind normal subgroups

Are normal subgroups transitive?

Finite group with isomorphic normal subgroups and non-isomorphic quotients?

Normal subgroups of $S_4$