Project ForgeDiscrete Mathematics
Set Theory & Abstract Algebra
GATE 2018
Medium
Let G be a finite group on 84 elements. The size of the largest possible proper subgroup of G is ____.
42
Explanation
By Lagrange's Theorem, the order of any subgroup must divide the order of the group (84). The largest PROPER divisor of 84 (excluding 84 itself) is 84 divided by its smallest prime factor, 2: 84/2 = 42.
Source: GATE CS 2018 (2018)
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