MATH 436 Notes: Sylow Theory
نویسنده
چکیده
We are now ready to apply the theory of group actions we studied in the last section to study the general structure of finite groups. A key role is played by the p-subgroups of a group. We will see that the Sylow theory will give us a way to study a group “a prime at a time”. First we record a very important special case of group actions: Theorem 1.1 (p-group Actions). Let p be a prime. If P is a p-group acting on a finite set X then |X| ≡ |X | mod p. Proof. By the orbit decomposition formula we have: |X| = |X |+ ∑
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