GATE Computer Science (CS) 2018 Shift 1 Solved Paper

Question : 26 of 65

Marks: +1, -0

Let

{G}

be a finite group on 84 elements. The size of a largest possible proper subgroup of

{G}

is ──────

Your Answer:

Validate

Solution:

Given

| {G}|=84

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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