GATE Algebra: Groups – Previous Year Questions
14 GATE previous year questions on Groups (Algebra, Mathematics) with answers and explanations, from every paper.
- GATE 2021 MA Q27 – Find the number of Sylow 5-subgroups of S₅.
- GATE 2021 MA Q54 – G has order 5⁴ and its center has 5² elements. Find the number of conjugacy classes.
- GATE 2022 MA Q26 – How many non-isomorphic abelian groups have order 2²·3³·5⁴?
- GATE 2022 MA Q27 – How many subgroups does a cyclic group of order 12 have?
- GATE 2023 MA Q36 – In GL₂(ℂ), let S=pmatrix0&-1\\1&0pmatrix, T₁=iI,T₂=diag(i,−i), T 3=pmatrix0&1\\1&0pmatrix and G j=⟨S,T j⟩. Write Z(G) for the center. Which holds?
- GATE 2023 MA Q54 – Let G be abelian and Φ:G→(ℤ,+) a surjective homomorphism, with Φ(a)=1. P:for every g∈G there is n∈ℤ with gaⁿ∈ker Φ. Q:G=(ker Φ)⟨a⟩ and (ker Φ)∩⟨a⟩=e.…
- GATE 2023 MA Q58 – In S₈, σ is the product of a disjoint 4-cycle and 3-cycle. How many permutations are conjugate to σ?
- GATE 2024 MA Q16 – For a group of order 2024, n p is its Sylow p-subgroup count. Which statement always holds?
- GATE 2024 MA Q27 – How many nonisomorphic finite groups have exactly three conjugacy classes? (integer)
- GATE 2024 MA Q31 – How many group homomorphisms ℤ/4ℤ→S₄ exist? (integer)
- GATE 2024 MA Q40 – I: Some proper subgroup G of (ℚ,+) has finite quotient ℚ/G. II: Some subgroup G has quotient isomorphic to (ℤ,+). Choose truth values.
- GATE 2025 MA Q64 – In a group G with identity e, g≠e, g²=e, h≠e, h²≠e and ghg⁻¹=h². Find the least positive n with hⁿ=e (integer).
- GATE 2026 MA Q14 – A group G has order 595. Which statement is true?
- GATE 2026 MA Q54 – Let G=ℤ₃₀⊕ℤ₁₂ under addition. Which statements hold?