Herstein's Restrictions

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This topic contains 2 replies, has 2 voices, and was last updated by  SaSA ::::: 6 days, 11 hours ago.

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  • #29357

    SaSA :::::
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    <p style=”text-align: left;”>Let G be a group of order pq, where p>q are primes. Prove that if q doesn’t divide p-1, then G is cyclic, without using Sylow theorems. (You can only use material developed up to section 2.9 of IN.Herstein.)</p>

    #29562

    Srijit Mukherjee
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    #29955

    SaSA :::::
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    Thanks, I saw this, but the problem is that Herstein has not introduced much of these ideas up to this problem. I found something different, it goes like this, center Z of G has order either 1 or pq, if q doesn’t divide p-1 it can be shown that a normal subgroup of order p is contained in Z, therefore Z=G, so G is abelian and it has an element of order pq.

    • This reply was modified 6 days, 11 hours ago by  SaSA :::::.
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