Sylow theorems
Let be a finite group whose order is divisible by the prime . Suppose is the highest power of which is a factor of and set
Then
-
1.
the group contains at least one subgroup of order ,
-
2.
any two subgroups of of order are conjugate, and
-
3.
the number of subgroups of of order is congruent to modulo and is a factor of .
Title | Sylow theorems |
---|---|
Canonical name | SylowTheorems |
Date of creation | 2013-03-22 12:24:12 |
Last modified on | 2013-03-22 12:24:12 |
Owner | yark (2760) |
Last modified by | yark (2760) |
Numerical id | 6 |
Author | yark (2760) |
Entry type | Theorem |
Classification | msc 20D20 |
Related topic | SylowPSubgroup |
Related topic | ApplicationOfSylowsTheoremsToGroupsOfOrderPq |
Related topic | SylowsFirstTheorem |
Related topic | SylowsThirdTheorem |
Related topic | SylowPSubgroups |