Difference between revisions of "Invariant subset"
From Encyclopedia of Mathematics
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| − | A subset $H$ of $G$ that contains | + | 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. |
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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=37452
Invariant subset. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Invariant_subset&oldid=37452
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article