Subgroup - Revision history

BrianMcMahon: Tidied translations.

2017-11-20T08:59:18Z

Tidied translations.

MassimoNespolo: two languages added

2017-10-10T15:29:38Z

two languages added

BrianMcMahon: Style edits to align with printed edition

2017-05-17T11:29:03Z

Style edits to align with printed edition

MassimoNespolo: /* See also */ ITA 6th edition

2017-04-11T16:52:31Z

‎See also: ITA 6th edition

BerndSouvignier at 10:46, 2 April 2009

2009-04-02T10:46:41Z

MassimoNespolo: /* See also */

2008-06-30T08:27:14Z

‎See also

MassimoNespolo: /* See also */

2007-04-25T17:56:01Z

‎See also

MassimoNespolo at 17:16, 25 April 2007

2007-04-25T17:16:36Z

MassimoNespolo: Category

2007-02-27T15:56:50Z

MassimoNespolo at 15:56, 27 February 2007

2007-02-27T15:56:13Z

New page

Sous-groupe (''Fr''); Untergruppe (''Ge''); Subgrupo (''Sp''); Sottogruppo (''It''); 部分群 (''Ja'').

Let G be a group and H a non-empty subset of G. Then H is called a '''subgroup''' of H if the elements of H obey the group postulates.

The subgroup H is called a ''proper subgroup'' of G if there are elements of G not contained in H.

A subgroup H of G is called a ''maximal subgroup'' of G if there is no proper subgroup M of G such that H is a proper subgroup of M.

==See also==
*[[ Normal subgroup]]
*Section 8.3.3 in the ''International Tables for Crystallography, Volume A''

← Older revision		Revision as of 08:59, 20 November 2017
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−	<font color="orange">زمرة جزئية</font> (''Ar''); <font color="blue">Sous-groupe</font> (''Fr''); <font color="red">Untergruppe</font> (''Ge''); <font color="black">Sottogruppo</font> (''It''); <font color="purple">部分群</font> (''Ja''); <font color="brown">Подгруппа</font> (''Ru''); <font color="green">Subgrupo</font> (''Sp'').	+	<font color="orange">زمرة جزئية</font> (''Ar''). <font color="blue">Sous-groupe</font> (''Fr''). <font color="red">Untergruppe</font> (''Ge''). <font color="black">Sottogruppo</font> (''It''). <font color="purple">部分群</font> (''Ja''). <font color="brown">Подгруппа</font> (''Ru''). <font color="green">Subgrupo</font> (''Sp'').

← Older revision		Revision as of 15:29, 10 October 2017
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−	<font color="blue">Sous-groupe</font> (''Fr''). <font color="red">Untergruppe</font> (''Ge''). <font color="~~green~~">~~Subgrupo~~</font> (''Sp''). <font color="~~black~~">~~Sottogruppo~~</font> (''It''). <font color="~~purple~~">~~部分群~~</font> (''Ja'').	+	<font color="orange">زمرة جزئية</font> (''Ar''); <font color="blue">Sous-groupe</font> (''Fr''); <font color="red">Untergruppe</font> (''Ge''); <font color="black">Sottogruppo</font> (''It''); <font color="purple">部分群</font> (''Ja''); <font color="brown">Подгруппа</font> (''Ru''); <font color="green">Subgrupo</font> (''Sp'').

@@ Line 1: / Line 1: @@
-<font color="blue">Sous-groupe</font> (''Fr''); <font color="red">Untergruppe</font> (''Ge''); <font color="green">Subgrupo</font> (''Sp''); <font color="black">Sottogruppo</font> (''It''); <font color="purple">部分群</font> (''Ja'').
+<font color="blue">Sous-groupe</font> (''Fr''). <font color="red">Untergruppe</font> (''Ge''). <font color="green">Subgrupo</font> (''Sp''). <font color="black">Sottogruppo</font> (''It''). <font color="purple">部分群</font> (''Ja'').
-Let ''G'' be a [[group]] and ''H'' a non-empty subset of ''G''. Then ''H'' is called a '''subgroup''' of ''G'' if the elements of ''H'' obey the group postulates, i.e. if
+Let ''G'' be a [[group]] and ''H'' a non-empty subset of ''G''. Then ''H'' is called a '''subgroup''' of ''G'' if the elements of ''H'' obey the group postulates, ''i.e.'' if
 # the identity element ''1<sub>G</sub>'' of ''G'' is contained in ''H'';
 # ''H'' is closed under the group operation (inherited from ''G'');
@@ Line 16: / Line 16: @@
 *[[Normal subgroup]]
 *[[Supergroup]]
-*Section 1.7.1 in the ''International Tables for Crystallography, Volume A'', 6<sup>th</sup> edition
+*Chapter 1.7.1 of ''International Tables for Crystallography, Volume A'', 6th edition
 [[Category:Fundamental crystallography]]

@@ Line 16: / Line 16: @@
 *[[Normal subgroup]]
 *[[Supergroup]]
-*Section 8.3.3 in the ''International Tables for Crystallography, Volume A''
+*Section 1.7.1 in the ''International Tables for Crystallography, Volume A'', 6<sup>th</sup> edition
 [[Category:Fundamental crystallography]]

@@ Line 12: / Line 12: @@
 *[[Coset]]
 *[[Normal subgroup]]
 *Section 8.3.3 in the ''International Tables for Crystallography, Volume A''
 [[Category:Fundamental crystallography]]

@@ Line 2: / Line 2: @@
-Let G be a group and H a non-empty subset of G. Then H is called a '''subgroup''' of H if the elements of H obey the group postulates.
+Let ''G'' be a [[group]] and ''H'' a non-empty subset of ''G''. Then ''H'' is called a '''subgroup''' of ''G'' if the elements of ''H'' obey the group postulates, i.e. if
-The subgroup H is called a ''proper subgroup'' of G if there are elements of G not contained in H.
+The subgroup ''H'' is called a '''proper subgroup''' of ''G'' if there are elements of ''G'' not contained in ''H''.
-A subgroup H of G is called a ''maximal subgroup'' of G if there is no proper subgroup M of G such that H is a proper subgroup of M.
+A subgroup ''H'' of ''G'' is called a '''maximal subgroup''' of ''G'' if there is no proper subgroup ''M'' of ''G'' such that ''H'' is a proper subgroup of ''M''.
 ==See also==

← Older revision		Revision as of 15:56, 27 February 2007
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	*[[ Normal subgroup]]		*[[ Normal subgroup]]
	*Section 8.3.3 in the ''International Tables for Crystallography, Volume A''		*Section 8.3.3 in the ''International Tables for Crystallography, Volume A''
		+
		+	[[Category:Fundamental crystallography]]