Function restriction formalism chart: Difference between revisions

Revision as of 18:35, 21 December 2007

Subgroup property	Expression	Endo-invariance	Balanced	Invariance	Left-inner	Quotient-hereditary invariance
Normal subgroup	Inner $\to$ Aut, Inner $\to$ Function	Yes	No	Yes	Yes	-	Characteristic subgroup	Aut $\to$ Aut, Aut $\to$ Function	Yes	Yes	Yes	No	-	Strictly characteristic subgroup	Surj. End $\to$ Function, Surj. End. $\to$ End.	Yes	No	Yes	No	- \|}

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 {| class="wikitable" border="1"
-! Subgroup property !! Expression !! Endo-invariance !! Balanced !! Invariance !! Left-inner !! Quotient-hereditary invariance |-
+! Subgroup property !! Expression !! Endo-invariance !! Balanced !! Invariance !! Left-inner !! Quotient-hereditary invariance
-[[Normal subgroup]] || Inner <math>\to</math> Aut, Inner <math>\to</math> Function || Yes || No || Yes || Yes || Yes |-
+|-
-[[Characteristic subgroup]] || Aut <math>\to</math> Aut, Aut <math>\to</math> Function || Yes || Yes || Yes || No || No |-
+|[[Normal subgroup]] || Inner <math>\to</math> Aut, Inner <math>\to</math> Function || Yes || No || Yes || Yes || Yes |-
-[[Strictly characteristic subgroup]] || Surj. End <math>\to</math> Function, Surj. End. <math>\to</math> End. || Yes || No || Yes || No || Yes |- |}
+|[[Characteristic subgroup]] || Aut <math>\to</math> Aut, Aut <math>\to</math> Function || Yes || Yes || Yes || No || No |-
+|[[Strictly characteristic subgroup]] || Surj. End <math>\to</math> Function, Surj. End. <math>\to</math> End. || Yes || No || Yes || No || Yes |- |}