GATE 2014 CS (CS3) – Question 13
A group G has 15 elements. L is a subgroup with $L\ne G$ and $|L|\ge4$. Find |L|.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 5 to 5
Explanation
Lagrange’s theorem makes the subgroup order a divisor of15:1,3,5or15. Being proper excludes15, while size at least4excludes1and3. Therefore **|L|=5**. No assumption that every divisor necessarily occurs is needed because existence is given.