ISI2020-MMA: 26

Question

For a cyclic group $\text{G}$ of order $12$, the number of subgroups of $\text{G}$ is

• A. $2$

• B. $6$

• C. $8$

• D. $11$

Comments

6 subgroups possible of sizes 1,2,3,4,6,12 as directly by lagrange theorem.

Answer 1

Lagrange's Theorem: In any finite group G, the order (number of elements) of every subgroup of G divides the order of G. 

Here G is the group with an order $12$.So it’s factor are: $1,2,3,4,6,12$

$\therefore 1,2,3,4,6,12$ six subgroups are there.

Lagrange's Theorem-based question:

• gate 2014
• gate 2018
• gate 2020