Gate2018 cs Q28

0. Let G be a finite group on 84 elements. The size of a largest possible proper subgroup of G is _________.

Note – Numerical Type question

Answer
Comment
Array

Option : B
Explanation :
Given |G| = 84
Solutions:
By Lagrang’s theorem any subgroup size is a divisior of 84.
But a proper subgroup cannot have same size as group.
So largest divisor of 84, other than 84 is 42.
So, largest proper subgroup can have in size of 42.

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