Order (group theory) - Revision history

BrianMcMahon: moved Order to Order (group theory): Disambiguation

2017-11-16T13:19:11Z

moved Order to Order (group theory): Disambiguation

BrianMcMahon: Tidied translations.

2017-11-16T13:18:38Z

Tidied translations.

MassimoNespolo: Lang (Ar)

2017-09-14T09:17:35Z

Lang (Ar)

MassimoNespolo: link

2017-05-21T05:29:17Z

link

BrianMcMahon: Style edits to align with printed edition

2017-05-16T10:30:29Z

Style edits to align with printed edition

MassimoNespolo: Precision

2014-12-08T13:08:07Z

Precision

MassimoNespolo: languages (Ja)

2014-06-05T11:11:08Z

languages (Ja)

MassimoNespolo: involution

2012-05-01T15:45:22Z

involution

BerndSouvignier: initial definition

2009-04-02T11:16:48Z

initial definition

New page

Ordre (''Fr''); Ordnung (''Ge''); Orden (''Sp''); Ordine (''It'').

If ''G'' is a [[group]] consisting of a finite number of elements, this number of elements is the '''order''' of ''G''. For example, the point group <tt>m3m</tt> has order 48.

For an element ''g'' of a (not necessarily finite) group ''G'', the '''order''' of ''g'' is the smallest integer ''n'' such that ''gn'' is the identity element of ''G''. If no such integer exists, ''g'' is of '''infinite order'''. For example, the rotoinversion <tt>3</tt> has order 6 and a translation has infinite order.

[[Category:Fundamental crystallography]]

← Older revision		Revision as of 13:18, 16 November 2017
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−	<font color="~~blue~~">~~Ordre~~</font> (''Fr''); <font color="~~red~~">~~Ordnung~~</font> (''Ge''); <font color="~~green~~">~~Orden~~</font> (''Sp''); <font color="black">Ordine</font> (''It''); <font color="purple">位数</font> (''Ja''); <font color="~~orange~~">~~نظام~~</font> (''Ar'').	+	<font color="orange">نظام</font> (''Ar''). <font color="blue">Ordre</font> (''Fr''). <font color="red">Ordnung</font> (''Ge''). <font color="black">Ordine</font> (''It''). <font color="purple">位数</font> (''Ja''). <font color="green">Orden</font> (''Sp'').

← Older revision		Revision as of 09:17, 14 September 2017
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−	<font color="blue">Ordre</font> (''Fr''). <font color="red">Ordnung</font> (''Ge''). <font color="green">Orden</font> (''Sp''). <font color="black">Ordine</font> (''It''). <font color="purple">位数</font> (''Ja'').	+	<font color="blue">Ordre</font> (''Fr''); <font color="red">Ordnung</font> (''Ge''); <font color="green">Orden</font> (''Sp''); <font color="black">Ordine</font> (''It''); <font color="purple">位数</font> (''Ja''); <font color="orange">نظام</font> (''Ar'').

← Older revision		Revision as of 05:29, 21 May 2017
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	If ''G'' is a [[group]] consisting of a finite number of elements, this number of elements is the '''order''' of ''G''. For example, the point group <tt>m<span style="text-decoration: overline">3</span>m</tt> has order 48.		If ''G'' is a [[group]] consisting of a finite number of elements, this number of elements is the '''order''' of ''G''. For example, the point group <tt>m<span style="text-decoration: overline">3</span>m</tt> has order 48.

−	For an element ''g'' of a (not necessarily finite) group ''G'', the '''order''' of ''g'' is the smallest integer ''n'' such that ''g<sup>n</sup>'' is the identity element of ''G''. If no such integer exists, ''g'' is of '''infinite order'''. For example, the rotoinversion <math>\bar 3</math> has order 6 and a translation has infinite order. An element of order 2 is its own inverse and is called an ~~'''~~involution~~'''~~.	+	For an element ''g'' of a (not necessarily finite) group ''G'', the '''order''' of ''g'' is the smallest integer ''n'' such that ''g<sup>n</sup>'' is the identity element of ''G''. If no such integer exists, ''g'' is of '''infinite order'''. For example, the rotoinversion <math>\bar 3</math> has order 6 and a translation has infinite order. An element of order 2 is its own inverse and is called an [[involution]].

@@ Line 1: / Line 1: @@
-<font color="blue">Ordre</font> (''Fr''); <font color="red">Ordnung</font> (''Ge''); <font color="green">Orden</font> (''Sp''); <font color="black">Ordine</font> (''It''); <font color="purple">位数</font> (''Ja'').
+<font color="blue">Ordre</font> (''Fr''). <font color="red">Ordnung</font> (''Ge''). <font color="green">Orden</font> (''Sp''). <font color="black">Ordine</font> (''It''). <font color="purple">位数</font> (''Ja'').
 If ''G'' is a [[group]] consisting of a finite number of elements, this number of elements is the '''order''' of ''G''. For example, the point group <tt>m<span style="text-decoration: overline">3</span>m</tt> has order 48.
-For an element ''g'' of a (not necessarily finite) group ''G'', the '''order''' of ''g'' is the smallest integer ''n'' such that ''g<sup>n</sup>'' is the identity element of ''G''. If no such integer exists, ''g'' is of '''infinite order'''. For example, the rotoinversion <tt><span style="text-decoration: overline">3</span></tt> has order 6 and a translation has infinite order. An element of order 2 is its own inverse and is called an '''involution'''.
+For an element ''g'' of a (not necessarily finite) group ''G'', the '''order''' of ''g'' is the smallest integer ''n'' such that ''g<sup>n</sup>'' is the identity element of ''G''. If no such integer exists, ''g'' is of '''infinite order'''. For example, the rotoinversion <math>\bar 3</math> has order 6 and a translation has infinite order. An element of order 2 is its own inverse and is called an '''involution'''.

← Older revision		Revision as of 13:08, 8 December 2014
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	If ''G'' is a [[group]] consisting of a finite number of elements, this number of elements is the '''order''' of ''G''. For example, the point group <tt>m<span style="text-decoration: overline">3</span>m</tt> has order 48.		If ''G'' is a [[group]] consisting of a finite number of elements, this number of elements is the '''order''' of ''G''. For example, the point group <tt>m<span style="text-decoration: overline">3</span>m</tt> has order 48.

−	For an element ''g'' of a (not necessarily finite) group ''G'', the '''order''' of ''g'' is the smallest integer ''n'' such that ''g<sup>n</sup>'' is the identity element of ''G''. If no such integer exists, ''g'' is of '''infinite order'''. For example, the rotoinversion <tt><span style="text-decoration: overline">3</span></tt> has order 6 and a translation has infinite order. An element of order 2 is called an '''involution'''.	+	For an element ''g'' of a (not necessarily finite) group ''G'', the '''order''' of ''g'' is the smallest integer ''n'' such that ''g<sup>n</sup>'' is the identity element of ''G''. If no such integer exists, ''g'' is of '''infinite order'''. For example, the rotoinversion <tt><span style="text-decoration: overline">3</span></tt> has order 6 and a translation has infinite order. An element of order 2 is its own inverse and is called an '''involution'''.

← Older revision	Revision as of 13:19, 16 November 2017
(No difference)

← Older revision		Revision as of 11:11, 5 June 2014
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−	<font color="blue">Ordre</font> (''Fr''); <font color="red">Ordnung</font> (''Ge''); <font color="green">Orden</font> (''Sp''); <font color="black">Ordine</font> (''It'').	+	<font color="blue">Ordre</font> (''Fr''); <font color="red">Ordnung</font> (''Ge''); <font color="green">Orden</font> (''Sp''); <font color="black">Ordine</font> (''It''); <font color="purple">位数</font> (''Ja'').

← Older revision		Revision as of 15:45, 1 May 2012
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	If ''G'' is a [[group]] consisting of a finite number of elements, this number of elements is the '''order''' of ''G''. For example, the point group <tt>m<span style="text-decoration: overline">3</span>m</tt> has order 48.		If ''G'' is a [[group]] consisting of a finite number of elements, this number of elements is the '''order''' of ''G''. For example, the point group <tt>m<span style="text-decoration: overline">3</span>m</tt> has order 48.

−	For an element ''g'' of a (not necessarily finite) group ''G'', the '''order''' of ''g'' is the smallest integer ''n'' such that ''g<sup>n</sup>'' is the identity element of ''G''. If no such integer exists, ''g'' is of '''infinite order'''. For example, the rotoinversion <tt><span style="text-decoration: overline">3</span></tt> has order 6 and a translation has infinite order.	+	For an element ''g'' of a (not necessarily finite) group ''G'', the '''order''' of ''g'' is the smallest integer ''n'' such that ''g<sup>n</sup>'' is the identity element of ''G''. If no such integer exists, ''g'' is of '''infinite order'''. For example, the rotoinversion <tt><span style="text-decoration: overline">3</span></tt> has order 6 and a translation has infinite order. An element of order 2 is called an '''involution'''.