Question 14345 – DSSSB PGT 2018 Female
April 29, 2024Engineering-Mathematics
April 29, 2024GATE 2021 CS-Set-1
|
Question 37
|
Which one of the following options is correct?
|
G is always cyclic, but H may not be cyclic.
|
|
|
Both G and H are always cyclic.
|
|
|
G may not be cyclic, but H is always cyclic.
|
|
|
Both G and H may not be cyclic.
|
If ‘G’ is a group with sides 6, its subgroups can have orders 1, 2, 3, 6.
(The subgroup order must divide the order of the group)
Given ‘H’ can be 1 to 6, but 4, 5 cannot divide ‘6’.
Then ‘H’ is not a subgroup.
G can be cyclic only if it is abelian. Thus G may or may not be cyclic.
The H can be cyclic only for the divisors of 6 and H cannot be cyclic for any non divisors of 6.
If ‘G’ is a group with sides 6, its subgroups can have orders 1, 2, 3, 6.
(The subgroup order must divide the order of the group)
Given ‘H’ can be 1 to 6, but 4, 5 cannot divide ‘6’.
Then ‘H’ is not a subgroup.
G can be cyclic only if it is abelian. Thus G may or may not be cyclic.
The H can be cyclic only for the divisors of 6 and H cannot be cyclic for any non divisors of 6.