Sylow p-subgroup
If is a group then any subgroup of order for any integer a is called a p-subgroup. If , where then any subgroup of with is a Sylow p-subgroup. We use for the set of Sylow p-groups of .
More generally, if is any group (not necessarily finite), a Sylow p-subgroup is a maximal -subgroup of .
Title | Sylow p-subgroup |
Canonical name | SylowPsubgroup |
Date of creation | 2013-03-22 12:50:59 |
Last modified on | 2013-03-22 12:50:59 |
Owner | Henry (455) |
Last modified by | Henry (455) |
Numerical id | 8 |
Author | Henry (455) |
Entry type | Definition |
Classification | msc 20D20 |
Synonym | Sylow subgroup |
Synonym | Sylow group |
Related topic | SylowTheorems |
Related topic | ProofOfSylowTheorems |
Related topic | PPrimaryComponent |
Related topic | SylowsThirdTheorem |
Defines | Sylow p-subgroup |
Defines | p-subgroup |