Project ForgeDiscrete Mathematics
Set Theory & Abstract Algebra
GATE 2020
Medium
Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is ____.
7
Explanation
By Lagrange's theorem, the order of any subgroup of G must divide |G| = 35 = 5×7. The divisors of 35 are 1, 5, 7, 35. Excluding G itself (order 35), the largest possible proper-subgroup order is 7.
Source: GATE CS 2020 (2020)
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