Namespaces
Variants
Actions

Difference between revisions of "Invariant subset"

From Encyclopedia of Mathematics
Jump to: navigation, search
(Category:Group theory and generalizations)
(MSC 20E45)
 
Line 1: Line 1:
{{TEX|done}}
+
{{TEX|done}}{{MSC|20E45}}
 +
 
 
''of a group $G$''
 
''of a group $G$''
  
A subset $H$ of $G$ that contains together with each element $h$ of it all [[Conjugate elements|conjugate elements]] of $h$ in $G$, that is, all elements of the form $g^{-1}hg$. An invariant sub-semi-group is a sub-semi-group that is at the same time an invariant subset.
+
A subset $H$ of $G$ the property that if it contains some element $h$ then it contains all [[conjugate elements]] of $h$ in $G$, that is, all elements of the form $g^{-1}hg$ for $g \in G$; hence, a subset which is a union of [[conjugacy class]]es of $G$. An invariant sub-semi-group is a sub-semi-group that is at the same time an invariant subset.
 
 
[[Category:Group theory and generalizations]]
 

Latest revision as of 17:45, 10 January 2016

2020 Mathematics Subject Classification: Primary: 20E45 [MSN][ZBL]

of a group $G$

A subset $H$ of $G$ the property that if it contains some element $h$ then it contains all conjugate elements of $h$ in $G$, that is, all elements of the form $g^{-1}hg$ for $g \in G$; hence, a subset which is a union of conjugacy classes of $G$. An invariant sub-semi-group is a sub-semi-group that is at the same time an invariant subset.

How to Cite This Entry:
Invariant subset. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Invariant_subset&oldid=34542
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article