I am confused as to whether Sylow refers to just subgroups or to groups as well. Every group is a subgroup of itself, so is that why it's called Sylow p-subgroup vs. just a Sylow p-group? Also, some of the examples were confusing to me especially following the Applications of the Sylow Theorems subtitle.
The most interesting part of this section was Corollary 8.18 because it seems as though it is a very helpful fact in figuring out what various groups are isomorphic to. Also I was wondering where the term Sylow came from. Is it named after a person?
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