New posts in normal-subgroups

How do I show a mapping is a homomorphism?

group-theory abstract-algebra normal-subgroups

Showing the product of two normal subgroups is normal [closed]

abstract-algebra normal-subgroups

Suppose $H$ is the only subgroup of order $o(H)$ in the finite group $G$. Prove that $H$ is a normal subgroup of $G$.

abstract-algebra group-theory normal-subgroups

Prove that there exists a $z \in Z(G)$ such that $yx = zxy$.

group-theory finite-groups normal-subgroups p-groups

Counterexample for the normalizer being a normal subgroup

abstract-algebra group-theory examples-counterexamples normal-subgroups

Give an example of a non abelian group $G$ and a subgroup $H\subset Z(G) $(proper subgroup) such that $H$ is not characteristic subgroup of $G$

group-theory examples-counterexamples normal-subgroups automorphism-group characteristic-subgroups

Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.

group-theory normal-subgroups

Equivalent definitions of normal subgroups

abstract-algebra group-theory normal-subgroups

Properties possessed by $H , G/H$ but not G

group-theory abelian-groups cyclic-groups normal-subgroups

Does $[G,G] \trianglelefteq \text{ker}(\Psi)$ hold?

group-theory normal-subgroups group-homomorphism

Finite normal subgroups of $\operatorname{SU}(n)$

group-theory finite-groups lie-groups normal-subgroups

Normal Subgroups in Group Theory

group-theory normal-subgroups

All subgroups normal $\implies$ abelian group

abelian-groups normal-subgroups

We Quotient an algebraic structure to generate equivalence classes?

abstract-algebra ideals equivalence-relations normal-subgroups

Prove Fitting's theorem for finite groups

group-theory finite-groups normal-subgroups nilpotent-groups

Any Subgroup containing commutator subgroup is normal.

abstract-algebra group-theory normal-subgroups derived-subgroup

Why are normal subgroups called "normal"?

abstract-algebra group-theory terminology math-history normal-subgroups

Commutator Group of $GL_2(R)$ is $SL_2(R)$

group-theory normal-subgroups linear-groups

Conjugacy class of $G$ splitting as Conjugacy class of $H\unlhd G$

abstract-algebra group-theory normal-subgroups

Where am I wrong that I can prove every subgroup is normal?

group-theory solution-verification group-actions normal-subgroups fake-proofs