Exponent of a finite group equals product of exponents of its Sylow subgroups

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Statement

Suppose G is a finite group and \{ p_1,p_2, \dots, p_r \} is the set of prime numbers dividing the order of G. For each p_i, let P_i be a p_i-Sylow subgroup of G. Then, we have:

\mbox{Exponent of } G = \prod_{i=1}^r (\mbox{exponent of } P_i)

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