GATE CSE 2020 Q28: Largest proper subgroup of a group of order 35
- Engineering Mathematics
- 1 mark
- NAT
- No negative marking
Question
Let be a group of 35 elements. Then the largest possible size of a subgroup of other than itself is _______.
Try it: numerical answer: type the value
Numerical answer. No negative marking.
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Answer: 7 (official GATE 2020 final answer key)
Concept used: Lagrange's theorem: the order of a subgroup divides the order of the group.
First step: List the divisors of 35 (1, 5, 7, 35) and take the largest one below 35.
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Source: official GATE 2020 CS question paper and final answer key, organised by IIT Delhi. Question paper · Answer key
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