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: Low Entry average rating: No information on entry rating
stabilizer (Definition)

Let $ G$ be a group, $ X$ a set, and $ \cdot: G \times X \longrightarrow X$ a group action. For any subset $ S$ of $ X$, the stabilizer of $ S$, denoted $ \operatorname{Stab}(S)$, is the subgroup

$\displaystyle \operatorname{Stab}(S) := \{g \in G \mid g\cdot s \in S$   for all $\displaystyle \ s \in S\}. $
The stabilizer of a single point $ x$ in $ X$ is often denoted $ G_x$.



"stabilizer" is owned by djao.
(view preamble)

View style:

Other names:  isotropy subgroup

Attachments:
conjugate stabilizer subgroups (Derivation) by Thomas Heye
Log in to rate this entry.
(view current ratings)

Cross-references: point, subgroup, subset, group action, group
There are 31 references to this entry.

This is version 3 of stabilizer, born on 2002-01-21, modified 2003-03-23.
Object id is 1518, canonical name is Stabilizer.
Accessed 6131 times total.

Classification:
AMS MSC: 20M30 (Group theory and generalizations :: Semigroups :: Representation of semigroups; actions of semigroups on sets)
 16W22 (Associative rings and algebras :: Rings and algebras with additional structure :: Actions of groups and semigroups; invariant theory)
Pending Errata and Addenda
None.
[ View all 2 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

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