GATE 2021 MA – Question 27

Algebra · Groups · 1 mark · Numerical answer

Find the number of Sylow 5-subgroups of S₅.

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Correct answer: 6 to 6

Explanation

There are (5−1)!=24 distinct 5-cycles. Each order-5 subgroup contains four nonidentity 5-cycles and distinct subgroups intersect only at the identity. Thus the number is 24/4=**6**.

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