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.
(A) 42
(B) 84
(C) 1
(D) 28
Answer: (A)
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.
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