# Group Theory MCQs Quiz with Answers in PDF

Group theory is a compulsory subject in mathematics and other science degrees. Most students are worried about group theory MCQs quiz papers and as well as competitive exams. So that’s why we are sharing past papers’ exam questions for better exam preparations. Every year most of the professors add the same questions which mostly appear in past papers.

## Group Theory MCQs Quiz.3

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Group Theory MCQs Quiz.3

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1. Choose the correct option for subgroups.

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2. {-1,1,i,-i} is a subgroup of?

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3. Let H and K be finite subgroups of a group G. Then O(HK) = -----?

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4. Let H₁, and H₂ be two distinct subgroups, each of order 2, of a finite group G. Let H be the smallest subgroup containing H₁ and H₂, then |H| = ----?

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5. The converse of Lagrange's theorem does not hold in ------?

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6. If H and K are subgroups of a group G with |H| = 12 and |K| = 16, then which of the following may be the order of H∩K?

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7. No of subgroups of G = < a, b : a⁴ = b² = (ab)²= e > is -----?

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8. Point out the group containing two commutative elements ( say a, b ) , b ≠ a⁻¹ such that |ab| < lcm (|a|,|b|)?

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9. Let a and b be elements of the group. If |a| = 24 and |b| = 10 , then |<a>∩<b>| = -----?

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10. The number of distinct left cos sets of H = < a² : a⁴ = e > in G = < a, b : a⁴ = b² = (ab)² = e > are?

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11. Let (G, .) be a group. Which of the following is not a subgroup of G?

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12. If G = < a, b : a⁴ = b² = (ab)² = e >. Then index of H = < b > in G is

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13. If H < G, a,b ∈ G then Ha = Hb if and only if?

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14. Let A be an Abelian group and F be a set of all elements of finite order in A. Then F is ----?

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15. The total number of subgroups of Dₙ?