Question:
Let G be a group of order 39 such that it has exactly one subgroup of order 3 and exactly one subgroup of order 13. Then, which one of the following statements is TRUE ?
Let G be a group of order 39 such that it has exactly one subgroup of order 3 and exactly one subgroup of order 13. Then, which one of the following statements is TRUE ?
Updated On: Aug 13, 2024
- G is necessarily cyclic
- G is abelian but need not be cyclic
- G need not be abelian
- G has 13 elements of order 13
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
The correct option is (A) : G is necessarily cyclic.
Was this answer helpful?
0
0
Top Questions on Groups
- Consider
\(𝐺 = \left\{𝑚 + 𝑛\sqrt2\ ∶\ 𝑚, 𝑛 ∈ \Z\right\}\)
as a subgroup of the additive group ℝ.
Which of the following statements is/are TRUE ? - The center Z(G) of a group G is defined as
z(G) = {x ∈ G ∶ xg = gx for all g ∈ G}.
Let |G| denote the order of G. Then, which of the following statements is/are TRUE for any group G ? - Which of the following statements is/are TRUE ?
- Consider the group G = {A ∈ M2 (ℝ): AAT = I2} with respect to matrix multiplication. Let
Z(G) = {A ∈ G : AB = BA, for all B ∈ G}.
Then, the cardinality of Z(G) is - The number of permutations in S4 that have exactly two cycles in their cycle decompositions is equal to ___________.
View More Questions
Questions Asked in IIT JAM MA exam
- For n ≥ 3, let a regular n-sided polygon Pn be circumscribed by a circle of radius Rn and let rn be the radius of the circle inscribed in Pn. Then
\(\lim\limits_{n \rightarrow \infin}(\frac{R_n}{r_n})^{n^2}\)
equals- IIT JAM MA - 2024
- Sequences and Series
- Consider the function f: ℝ → ℝ given by f(x) = x3 - 4x2 + 4x - 6.
For c ∈ ℝ, let
\(S(c)=\left\{x \in \R : f(x)=c\right\}\)
and |S(c)| denote the number of elements in S(c). Then, the value of
|S(-7)| + |S(-5)| + |S(3)|
equals _________- IIT JAM MA - 2024
- Functions of One Real Variable
- For a > b > 0, consider
\(D=\left\{(x,y,z) \in \R^3 :x^2+y^2+z^2 \le a^2\ \text{and } x^2+y^2 \ge b^2\right\}.\)
Then, the surface area of the boundary of the solid D is- IIT JAM MA - 2024
- Functions of Two or Three Real Variables
- Consider the 4 × 4 matrix
\(M = \begin{pmatrix} 0 & 1 & 2 & 3 \\ 1 & 0 & 1 & 2 \\ 2 & 1 & 0 & 1 \\ 3 & 2 & 1 & 0 \end{pmatrix}\)
If ai,j denotes the (i, j)th entry of M-1 , then a4,1 equals __________ (rounded off to two decimal places).- IIT JAM MA - 2024
- Matrices
- Let
S = {f: ℝ → ℝ ∶ f is a polynomial and f(f(x)) = (f(x))2024 for x ∈ ℝ}.
Then, the number of elements in S is _____________- IIT JAM MA - 2024
- Functions of One Real Variable
View More Questions