PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (210)
Orphanage
Unclass'd (1)
Unproven (472)
Corrections (38)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Legalese
About
Owner confidence rating: Very low Entry average rating: Low
Sylow p-subgroup (Definition)

If $ (G,*)$ is a group then any subgroup of order $ p^a$ for any integer a is called a p-subgroup. If $ \vert G\vert=p^am$, where $ p\nmid m$ then any subgroup $ S$ of $ G$ with $ \vert S\vert=p^a$ is a Sylow p-subgroup. We use $ {\rm Syl_p}(G)$ for the set of Sylow p-groups of $ G$.

More generally, if $ G$ is any group (not necessarily finite), a Sylow p-subgroup is a maximal $ p$-subgroup of $ G$.



"Sylow p-subgroup" is owned by Henry.
(view preamble)

View style:

See Also: Sylow theorems, proof of Sylow theorems, p-primary component, Sylow's third theorem

Other names:  Sylow subgroup, Sylow group
Also defines:  Sylow p-subgroup, p-subgroup
Keywords:  Sylow, p-subgroup
Log in to rate this entry.
(view current ratings)

Cross-references: maximal, finite, p-groups, p-subgroup, integer, order, subgroup, group
There are 17 references to this entry.

This is version 5 of Sylow p-subgroup, born on 2002-07-22, modified 2007-08-20.
Object id is 3181, canonical name is SylowPSubgroup.
Accessed 8884 times total.

Classification:
AMS MSC: 20D20 (Group theory and generalizations :: Abstract finite groups :: Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure)
Pending Errata and Addenda
None.
[ View all 3 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)