List of Top Mathematical Science Questions on Group & Subgroups

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R 

Assertion A: The order of the group $(Z_5, \times)$ divides the order of the group $(Z_{13}, \times)$ 

Reason R: The order of a subgroup of a group divides the order of the group. 

In the light of the above statements, choose the most appropriate answer from the options given below

Let p be a prime number. Let G be a group such that for each g ∈ G there exists an n ∈ ℕ such that g^pn = 1. Which of the following statements is FALSE?

Let G = {1, -1, i, -i} be the multiplication group, and H = {1. -1} is a subgroup of G, then

Let H be a subgroup of a group G and K be a normal subgroup of a group G, then

Let G be the group (under matrix multiplication) of 2 × 2 invertible matrices with entries from /9ℤ. Let a be the order of G. Which of the following statements are true?

Which of the following statements are correct?

Let G be a group of order 24. Which of the following statements are necessarily true?

Let G be a finite group. Which of the following are true?

Let SL₂(\(\mathbb{Z}\)) = \(\left\{\left(\begin{array}{ll}a & b \\ c & d\end{array}\right) \in M_2(\mathbb{Z}): a d-b c=1\right\}\) and for any prime p, let

Γ(p) = \(\left\{\left(\begin{array}{ll}a & b \\ c & d\end{array}\right) \in SL_2(\mathbb{Z})| \begin{aligned} &a \equiv 1(\bmod p), d \equiv 1(\bmod p) \\ &c \equiv 0(\bmod p), b \equiv 0(\bmod p) \end{aligned}\right\}\)

Which of the following are true?

Which of the following statements are true?