Question:
No. of group homomorphism from Z4 to S4
No. of group homomorphism from Z4 to S4
Updated On: Jul 25, 2024
Hide Solution
Verified By Collegedunia
Correct Answer: 16
Solution and Explanation
The correct answer is 16
Was this answer helpful?
0
0
Top GATE MA Linear Algebra Questions
Consider P: Let \( M \in \mathbb{R}^{m \times n} \) with \( m>n \geq 2 \). If \( \text{rank}(M) = n \), then the system of linear equations \( Mx = 0 \) has \( x = 0 \) as the only solution. Q: Let \( E \in \mathbb{R}^{n \times n}, n \geq 2 \) be a non-zero matrix such that \( E^3 = 0 \). Then \( I + E^2 \) is a singular matrix. Which of the following statements is TRUE?
- GATE MA - 2022
- Linear Algebra
- Linear Algebra
- Suppose that the characteristic equation of \( M \in \mathbb{C}^{3 \times 3} \) is \[ \lambda^3 + \alpha \lambda^2 + \beta \lambda - 1 = 0, \] where \( \alpha, \beta \in \mathbb{C} \) with \( \alpha + \beta \neq 0 \).
Which of the following statements is TRUE?
- GATE MA - 2022
- Linear Algebra
- Matrix algebra
- Consider the linear system of equations \( Ax = b \) with
\[ A = \begin{pmatrix} 3 & 1 & 1 \\ 1 & 4 & 1 \\ 2 & 0 & 3 \end{pmatrix}, \quad b = \begin{pmatrix} 2 \\ 3 \\ 4 \end{pmatrix}. \] Which of the following statements are TRUE?
- GATE MA - 2022
- Linear Algebra
- Linear Systems and Determinants
- Consider the following conditions on two proper non-zero ideals \( J_1 \) and \( J_2 \) of a non-zero commutative ring \( R \): P: For any \( r_1, r_2 \in R \), there exists a unique \( r \in R \) such that \( r - r_1 \in J_1 \) and \( r - r_2 \in J_2 \). Q: \( J_1 + J_2 = R \) Then, which of the following statements is TRUE?
- GATE MA - 2022
- Linear Algebra
- Group Theory
- Let \( \mathbb{R}[X] \) denote the ring of polynomials in \( X \) with real coefficients. Then, the quotient ring \( \mathbb{R}[X]/(X^4 + 4) \) is
- GATE MA - 2022
- Linear Algebra
- Symmetric, Skew-Symmetric, Hermitian, Skew-Hermitian, Normal, Orthogonal and Unitary Matrices
View More Questions
Top GATE MA Symmetric, Skew-Symmetric, Hermitian, Skew-Hermitian, Normal, Orthogonal and Unitary Matrices Questions
- Let \( \mathbb{R}[X] \) denote the ring of polynomials in \( X \) with real coefficients. Then, the quotient ring \( \mathbb{R}[X]/(X^4 + 4) \) is
- GATE MA - 2022
- Linear Algebra
- Symmetric, Skew-Symmetric, Hermitian, Skew-Hermitian, Normal, Orthogonal and Unitary Matrices
Top GATE MA Questions
- If two events $A$ and $B$ are independent, then:
- GATE MA - 2026
- Probability
- Which method is commonly used to find roots of nonlinear equations?
- GATE MA - 2026
- Calculus
- Let $A$ be a square matrix. If $A^2 = A$, then the matrix $A$ is called:
- GATE MA - 2026
- Linear Programming
- The limit $\displaystyle \lim_{x \to 0} \frac{\sin x}{x}$ is equal to:
- GATE MA - 2026
- Calculus
- A continuous function on a closed and bounded interval is always:
- GATE MA - 2026
- Calculus
View More Questions