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Difference between revisions of "Invariant subgroup"

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The same as a [[Normal subgroup|normal subgroup]], that is, a subgroup <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i052/i052300/i0523001.png" /> of a group <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i052/i052300/i0523002.png" /> that is taken to itself under any [[Inner automorphism|inner automorphism]] of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i052/i052300/i0523003.png" />.
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The same as a [[Normal subgroup|normal subgroup]], that is, a subgroup $H$ of a group $G$ that is taken to itself under any [[Inner automorphism|inner automorphism]] of $G$.

Latest revision as of 07:14, 15 July 2014

The same as a normal subgroup, that is, a subgroup $H$ of a group $G$ that is taken to itself under any inner automorphism of $G$.

How to Cite This Entry:
Invariant subgroup. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Invariant_subgroup&oldid=16417