GATE 2022 MA – Question 26

Algebra · Groups · 1 mark · Numerical answer

How many non-isomorphic abelian groups have order 2²·3³·5⁴?

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Correct answer: 30 to 30

Explanation

The classification of finite abelian groups gives one choice for each partition of the prime exponent. The partition counts are p(2)=2,p(3)=3,p(4)=5. Independent primary factors give 2×3×5=**30**.

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