GATE 2024 MA – Question 16

Algebra · Groups · 1 mark · Multiple choice

For a group of order 2024, n_p is its Sylow p-subgroup count. Which statement always holds?

n₁₁=1,n₂₃=11
n₁₁∈{1,23},n₂₃=1
n₁₁=23,n₂₃∈{1,88}
n₁₁=23,n₂₃=11

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Show answer and explanation

Correct answer: (B) n₁₁∈{1,23},n₂₃=1

Explanation

Factor 2024=8×11×23. n₂₃ divides 88 and is 1 modulo 23; among divisors 1,2,4,8,11,22,44,88 only 1 qualifies. n₁₁ divides 184=8×23 and is 1 modulo 11; only 1 and 23 qualify. **B**.

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