List of top Mathematics Questions on Algebra asked in CUET (PG)

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:

Which of the following statements are correct:
A. Permutation group $S_n$ has order $n!$, $n > 1$.
B. Alternating group $A_n$ of degree $n$ has order $\frac{n!}{2}$, $n > 1$. C. Set of all even permutations forms a subgroup of $S_n$.
D. Every permutation in $S_n$, $n > 1$ is a product of 2-cycles.
E. $A_4$ has a subgroup of order 6.
Choose the correct answer from the options given below:

The generators of the set of integers $\mathbb{Z}$ under addition is:

Which of the following set forms a group under multiplication:

The integral domain of which cardinality is not possible:
A. 5
B. 6
C. 7
D. 10

Which one of the following mathematical structure forms a group?