Sylow theorem and further results

Sylow theorem and further results
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We prove the following facts based on previous Sylow main theorems:

0:00 start
6:00 the sylow group is normal iff it is the only one sylow
9:00 sylow group is the only sylow in its normalizer
11:00 every P subgroup is a subgroup of some sylow group
16:00 if one group contains a normalizer of some sylow group, then it is its own normalizer
20:20 a p group is not sylow can not be its normalizer

Advanced mathematics list:

Group representation for finite group
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