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Difference between revisions of "Invariant subset"

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''of a group <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i052/i052310/i0523101.png" />''
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''of a group $G$''
  
A subset <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i052/i052310/i0523102.png" /> of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i052/i052310/i0523103.png" /> that contains together with each element <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i052/i052310/i0523104.png" /> of it all [[Conjugate elements|conjugate elements]] of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i052/i052310/i0523105.png" /> in <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i052/i052310/i0523106.png" />, that is, all elements of the form <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i052/i052310/i0523107.png" />. An invariant sub-semi-group is a sub-semi-group that is at the same time an invariant subset.
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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.

Revision as of 15:56, 9 April 2014

of a group $G$

A subset $H$ of $G$ that contains together with each element $h$ of it all 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.

How to Cite This Entry:
Invariant subset. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Invariant_subset&oldid=11995
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article