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List Question

Intersection of two subgroups is a normal subgroup of another Intersection of two subgroups

Group which can be written as a union of proper normal subgroups

Are Cosets Isomorphic to One Another

Does $G\cong H\times K$ imply $H\unlhd G?$

Conjugacy classes of a quotient group

Proving $H$ is a normal subgroup of $G$

Let $A,B\le G$ be two abelian subgroups. Suppose that $G=\langle A\cup B\rangle$. Prove that $A\cap B \trianglelefteq G$.

Question on Artin Proof of The Classification of The Groups of Order $12$

How the existence of a special homomorphism of a group can help me constract a special normal subgroup to represent uniquely the group?

Example of conjugacy class where both are not real.

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Show that $G = M \circledast N$ has a diagonal subgroup iff $M$ is isomorphic to $N$.

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set of nth-power elements of a finite abelian group

Prove that L is a subset of M

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