Question 14345 – DSSSB PGT 2018 Female
April 29, 2024Question 14240 – Engineering-Mathematics
April 29, 2024Question 14236 – Engineering-Mathematics
Let G be a group of order 6, and H be a subgroup of G such that 1 < |H| < 6.
Which one of the following options is correct?
Correct Answer: D
Question 6 Explanation:
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.
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.
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