how many 2-sylow's subgroups are there in group of order 72. please explain
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72 = 2^{3}*3^{2}, so the 2-sylow subgroups are of order 8. the number of such subgroups is congruent to 1 mod 2, and is a divisor of 72. so the only possibilities are odd divisors of 72: 1,3 or 9.
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