GATE | GATE CS 2018 | Question 16
Let G be a finite group on 84 elements. The size of a largest possible proper subgroup of G is _______ .
Note – This was Numerical Type question.
Explanation: According to Lagrange’s theorem, states that for any finite group G, the order (number of elements) of every subgroup H of G divides the order of G.
Therefore, possible subgroups of group on 84 elements are : 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
Subgroups with element 1 and 84 are trivial groups.
The size of a largest possible proper subgroup of G is 42.
Quiz of this Question
Attention reader! Don’t stop learning now. Practice GATE exam well before the actual exam with the subject-wise and overall quizzes available in GATE Test Series Course.
Learn all GATE CS concepts with Free Live Classes on our youtube channel.