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Let $G$ be a finite group and $M(G)$ be the Schur multiplier of $G$. Show that the exponent $\exp(G)$ of $G$ divides the product of the exponents $\exp(M(S_p))$ of the Sylow $p$-subgroups $S_p$ of $G$.

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    what is your question? What are you having trouble with?2012-10-26
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    maybe, use transfer2012-10-26
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    It really depends on what results about Schur Multipliers you know already. For example do you know any results already that relate the $p$-part of $M(G)$ to $M(S_p)$?2012-10-26
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    note that every sylow p-subgroup of M(G) is isomorphism with some subgroup of M(Sp)2012-10-26
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    M(G) is abelian group and every abelian groups is direct sum of its sylow subgroups.2012-10-26
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    If you know that every Sylow $p$-subgroup of $M(G)$ is isomorphic with a subgroup of $M(S_p)$, then then $M(G)$ is isomorphic to the direct product of all of its Sylow $p$-subgroups, and you should be able to solve the problem.2012-10-27

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