show that there is a normal subgroup of G of order 5 when G is a group of order 30. My friend just called me with this problem, he said the usual method of solution fails. (i.e. using sylow and then showing that the subgroup is unique and deducing that it must therfore be normal), I told him to post it on physics forum so ytou might get this question twice.(adsbygoogle = window.adsbygoogle || []).push({});

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# Failure of the sylow counting argument

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