GATE | GATE CS 2020 | Question 28
Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is ________ .
Note – This question was Numerical Type.
Explanation: According to the Lagrange’s Theorem:
“If H is a subgroup of finite group G then the order of subgroup H divides the order of group G.”
Order of subgroup must be factor of Order of group.
Since order of a group is number of elements present in that group, therefore order of given group will be 35.
Factor of 35 are: 1, 5, 7, 35.
So, largest possible size of a subgroup of G other than G itself is 7.
Size of group = Ο(G) = 35 Let H be subgroup of G ∴ Ο(H)⏐Ο(G) Possible orders of H are 1, 5, 7, 35 Size of largest possible proper subgroup = 7.
Option (C) is correct.
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