GATE CS 2014 Set 3 — Question 13
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Engineering Mathematics → Sets & Combinatorics → Groups, Rings & Fields
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Question
Let be a group with 15 elements. Let be a subgroup of . It is known that and that the size of is at least 4. The size of is __________.
Correct answer
5 to 5
Solution
According to Lagrange's Theorem, the order (size) of a subgroup must divide the order of the group .Given .
The divisors of 15 are 1, 3, 5, and 15.Conditions given:
The divisors of 15 are 1, 3, 5, and 15.Conditions given:
1..
2.Size of is at least 4 .
Checking the divisors:- 1: (False)
- 3: (False)
- 5: (True) and (True)
- 15: (False, since )
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