Question

Which of the following statements are correct:
A. Subgroup $H$ of a group $G$ is normal in $G$ if $xHx^{-1} \subseteq H$ $\forall x \text{ in } G$ B. A subgroup of an abelian group is not normal.
C. Centre $Z(G)$ of a group $G$ is normal.
D. Every subgroup of an abelian group is normal.
E. Centre $Z(G)$ of a group $G$ is not normal.
Choose the correct answer from the options given below:

• A. A, B, C Only
• B. B, C, E Only
• C. A, C, D Only
• D. C, D Only

Hint:

Every subgroup of an abelian group is automatically normal! Also, $Z(G)$ is always a normal subgroup for any group $G$.

Answer 1

The Correct Option is C