New posts in normal-subgroups

Is it true that for a Group $G$ with Normal Group $N: G/N = GN/N$?

If $G$ is non-abelian, then $Inn(G)$ is not a normal subgroup of the group of all bijective mappings $G \to G$

Are all normal subgroups Abelian?

Questions on Proofs - Equivalent Conditions of Normal Subgroup - Fraleigh p. 141 Theorem 14.13

Let $|G|=735$. If the number of Sylow $7$-subgroups are more than $1$, then show that there exists a normal Sylow $5$-subgroup.

Characterization of nilpotency with normal subgroups

Commutator subgroup and subgroup generated by square.

Proving that a normal, abelian subgroup of G is in the center of G if |G/N| and |Aut(N)| are relatively prime.

Show that SO(n) is a normal subgroup of O(n)

Let $G$ be a group and let $H_1,H_2\unlhd G$ such that $H_1\cap H_2 = \{1\}$ and $H_1H_2=G.$ Prove $G\simeq H_1\times H_2$ [duplicate]

Group containing no subgroup of index 2 [closed]

Between the center of a quotient group and the total center

Why are there 5 subgroups that are generated by double transpositions on four elements in $S_5$?

Proof that normalizer and center are subgroups

How to describe all normal subgroups of the dihedral group Dn? [duplicate]

Show that if $|G|=30$ then $G$ has normal $3$-Sylow and $5$-Sylow

Group of order $1225$ is abelian

Prove that any subgroup of the center $Z(G)$ of $G$ is a normal subgroup of $G$.

Proving that a subgroup is normal if two equivalence relations on $A$ coincide

If $N,K$ are two finite groups with isomorphic subgroups, show $ X \leq N \times K $ is normal.