For ten points, identify these three fundamental results from  nite group theory, named after a Norwegian mathematician who also names maximal p-subgroups.
These statements can be used to prove that there is only one group with 15 elements, and the third of these statements leads to an easy proof of Wilson's theorem. The second of these statements claims for any p that all maximal p- subgroups of a group are conjugate to each other. The  rst of these statements strengthens Cauchy's theorem, and claims that for every prime factor p with multiplicity n of the order of a group, there exists a   maximal p-subgroup with order pn. For ten points, identify these three fundamental results from  nite group theory, named after a Norwegian mathematician who also names maximal p-subgroups.
These statements can be used to prove that there is only one group with 15 elements, and the third of these statements leads to an easy proof of Wilson's theorem.
Sylow's theorems  