Stabilizer - Revision history

MassimoNespolo: Not necessarily "sub" (部分)

2018-11-28T16:06:05Z

Not necessarily "sub" (部分)

BrianMcMahon: Tidied translations.

2017-11-20T08:49:46Z

Tidied translations.

MassimoNespolo: languages

2017-10-13T12:42:00Z

languages

BrianMcMahon: Style edits to align with printed edition

2017-05-17T11:03:45Z

Style edits to align with printed edition

MassimoNespolo: /* Example */

2007-02-28T11:42:58Z

‎Example

MassimoNespolo at 15:44, 27 February 2007

2007-02-27T15:44:12Z

New page

Stabilisateur (''Fr''); Stabilisator (''Ge''); Stabilizzatore (''It''); 安定部分群 (''Ja'').

Let G be a group which acts on a set A by a composition law *, and let ''a'' be a given element of A. Then the set:

G''a'' = {g ∈ G | ''a''*g = ''a''}

is called the '''stabilizer''' of A. G''a'' is the set of all elements of G which leave ''a'' unchanged or 'stable'. G''a'' is a [[subgroup]] of G.

==Example==
The [[site symmetry|site-symmetry group]] of a [[Wyckoff position]] is the stabilizer of that position.

==See also==
*[[Centralizer]]
*[[Normalizer]]

[[Category:Fundamental crystallography]]

← Older revision		Revision as of 16:06, 28 November 2018
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−	<font color="blue">Stabilisateur</font> (''Fr''). <font color="red">Stabilisator</font> (''Ge''). <font color="black">Stabilizzatore</font> (''It''). <font color="purple">~~安定部分群~~</font> (''Ja''). <font color="brown">Стабилизатор</font> (''Ru''). <font color="green">Estabilizador</font> (''Sp'').	+	<font color="blue">Stabilisateur</font> (''Fr''). <font color="red">Stabilisator</font> (''Ge''). <font color="black">Stabilizzatore</font> (''It''). <font color="purple">安定群</font> (''Ja''). <font color="brown">Стабилизатор</font> (''Ru''). <font color="green">Estabilizador</font> (''Sp'').

← Older revision		Revision as of 08:49, 20 November 2017
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−	<font color="blue">Stabilisateur</font> (''Fr''); <font color="red">Stabilisator</font> (''Ge''); <font color="black">Stabilizzatore</font> (''It''); <font color="purple">安定部分群</font> (''Ja''); <font color="brown">Стабилизатор</font> (''Ru''); <font color="green">Estabilizador</font> (''Sp'').	+	<font color="blue">Stabilisateur</font> (''Fr''). <font color="red">Stabilisator</font> (''Ge''). <font color="black">Stabilizzatore</font> (''It''). <font color="purple">安定部分群</font> (''Ja''). <font color="brown">Стабилизатор</font> (''Ru''). <font color="green">Estabilizador</font> (''Sp'').
		+
		+
		+	Synonym: isotropy group.

← Older revision		Revision as of 12:42, 13 October 2017
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−	<font color="blue">Stabilisateur</font> (''Fr''). <font color="red">Stabilisator</font> (''Ge''). <font color="black">Stabilizzatore</font> (''It''). <font color="purple">安定部分群</font> (''Ja'').	+	<font color="blue">Stabilisateur</font> (''Fr''); <font color="red">Stabilisator</font> (''Ge''); <font color="black">Stabilizzatore</font> (''It''); <font color="purple">安定部分群</font> (''Ja''); <font color="brown">Стабилизатор</font> (''Ru''); <font color="green">Estabilizador</font> (''Sp'').

@@ Line 1: / Line 1: @@
-<font color="blue">Stabilisateur</font> (''Fr''); <font color="red">Stabilisator</font> (''Ge''); <font color="black">Stabilizzatore</font> (''It''); <font color="purple">安定部分群</font> (''Ja'').
+<font color="blue">Stabilisateur</font> (''Fr''). <font color="red">Stabilisator</font> (''Ge''). <font color="black">Stabilizzatore</font> (''It''). <font color="purple">安定部分群</font> (''Ja'').
-Let G be a group which acts on a set A by a composition law *, and let ''a'' be a given element of A. Then the set:
+Let ''G'' be a group which acts on a set ''A'' by a composition law *, and let ''a'' be a given element of ''A''. Then the set
-G<sub>''a''</sub> = {g &isin; G | ''a''*g = ''a''}
+''G''<sub>''a''</sub> = {''g'' &isin; ''G'' | ''a''*g = ''a''}
-is called the '''stabilizer''' of A. G<sub>''a''</sub> is the set of all elements of G which leave ''a'' unchanged or 'stable'. G<sub>''a''</sub> is a [[subgroup]] of G.
+is called the '''stabilizer''' of ''A''. ''G''<sub>''a''</sub> is the set of all elements of ''G'' which leave ''a'' unchanged or 'stable'. ''G''<sub>''a''</sub> is a [[subgroup]] of ''G''.
 ==Example==
-The [[site symmetry|site-symmetry group]] of a [[Wyckoff position]] is the stabilizer of that position.  In this example, G is the [[space group]], the stabilizer is the [[site symmetry|site-symmetry group]], the set A is the set of triples of ''x'',''y'',''z'' coordinates (set of points in the three-dimensional space), the element ''a'' that is "stable" under the action of the stabilizer is the [[Wyckoff position]] which corresponds to that [[site symmetry|site-symmetry group]].
+The [[site symmetry|site-symmetry group]] of a [[Wyckoff position]] is the stabilizer of that position.  In this example, ''G'' is the [[space group]], the stabilizer is the [[site symmetry|site-symmetry group]], the set ''A'' is the set of triples of ''x'',''y'',''z'' coordinates (set of points in the three-dimensional space), the element ''a'' that is 'stable' under the action of the stabilizer is the [[Wyckoff position]] which corresponds to that [[site symmetry|site-symmetry group]].
 ==See also==