Tour:Sufficiency of subgroup criterion - Revision history

Vipul at 17:47, 29 August 2008

2008-08-29T17:47:37Z

← Older revision		Revision as of 17:47, 29 August 2008
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	__NOTOC__		__NOTOC__
	{{derivative of\|sufficiency of subgroup criterion}}		{{derivative of\|sufficiency of subgroup criterion}}
	{{~~guided~~ tour\|beginners\|~~Introduction~~ two\|Manipulating equations in groups\|Subsemigroup of finite group is subgroup}}		{{tour-regular\|
			target = beginners\|
			secnum = two\|
			next = Manipulating equations in groups\|
			previous = Subsemigroup of finite group is subgroup\|
			expected time = 8 minutes}}
	{{quotation\|'''WHAT YOU NEED TO DO''':		{{quotation\|'''WHAT YOU NEED TO DO''':
	* Recall the [[~~Guided tour for beginners~~:Subgroup\|various definitions of subgroup]], including the subgroup criterion		* Recall the [[Tour:Subgroup\|various definitions of subgroup]], including the subgroup criterion
	* Try proving that the subgroup criterion is necessary and sufficient		* Try proving that the subgroup criterion is necessary and sufficient
	* Read below the proof of sufficiency		* Read below the proof of sufficiency
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	* In what ways are things different for finite groups, and why?}}		* In what ways are things different for finite groups, and why?}}
	{{#lst:Sufficiency of subgroup criterion\|main}}		{{#lst:Sufficiency of subgroup criterion\|main}}
	{{~~guided~~ tour-bottom\|beginners\|~~Introduction~~ two\|Manipulating equations in groups\|Subsemigroup of finite group is subgroup}}		{{tour-regular-bottom\|
			target = beginners\|
			secnum = two\|
			next = Manipulating equations in groups\|
			previous = Subsemigroup of finite group is subgroup}}

Vipul: Guided tour for beginners:Sufficiency of subgroup criterion moved to Tour:Sufficiency of subgroup criterion

2008-06-20T20:03:38Z

Guided tour for beginners:Sufficiency of subgroup criterion moved to Tour:Sufficiency of subgroup criterion

← Older revision	Revision as of 20:03, 20 June 2008
(No difference)

Vipul at 14:10, 3 June 2008

2008-06-03T14:10:33Z

← Older revision		Revision as of 14:10, 3 June 2008
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	* In what ways are things different for finite groups, and why?}}		* In what ways are things different for finite groups, and why?}}
	{{#lst:Sufficiency of subgroup criterion\|main}}		{{#lst:Sufficiency of subgroup criterion\|main}}
			{{guided tour-bottom\|beginners\|Introduction two\|Manipulating equations in groups\|Subsemigroup of finite group is subgroup}}

Vipul at 14:10, 3 June 2008

2008-06-03T14:10:06Z

← Older revision		Revision as of 14:10, 3 June 2008
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	{{derivative of\|sufficiency of subgroup criterion}}		{{derivative of\|sufficiency of subgroup criterion}}
	{{guided tour\|beginners\|Introduction two\|Manipulating equations in groups\|Subsemigroup of finite group is subgroup}}		{{guided tour\|beginners\|Introduction two\|Manipulating equations in groups\|Subsemigroup of finite group is subgroup}}
	{{quotation\|~~This is a general condition for a nonempty subset to be a subgroup. We only check for left quotients of elements. The criterion isn~~'~~t used very frequently, but it is of theoretical importance for some applications. Proceed to~~ [[Guided tour for beginners:~~Manipulating equations in groups~~]] ~~OR Return to [[Guided tour~~ for ~~beginners~~:~~Subsemigroup~~ of finite ~~group is subgroup]]~~}}		{{quotation\|'''WHAT YOU NEED TO DO''':
			* Recall the [[Guided tour for beginners:Subgroup\|various definitions of subgroup]], including the subgroup criterion
			* Try proving that the subgroup criterion is necessary and sufficient
			* Read below the proof of sufficiency
			* Compare with the result we just saw for finite groups (any nonempty multiplicatively closed subset is a subgroup)<br>
			'''PONDER''':
			* What axioms of group structure play a role in this proof?
			* In what ways are things different for finite groups, and why?}}
	{{#lst:Sufficiency of subgroup criterion\|main}}		{{#lst:Sufficiency of subgroup criterion\|main}}

Vipul at 14:11, 18 May 2008

2008-05-18T14:11:09Z

@@ Line 1: / Line 1: @@
 __NOTOC__
-{{derivative of|sufficiency of subgroup condition}}
+{{derivative of|sufficiency of subgroup criterion}}
 {{guided tour|beginners|Introduction two|Manipulating equations in groups|Subsemigroup of finite group is subgroup}}
 {{quotation|This is a general condition for a nonempty subset to be a subgroup. We only check for left quotients of elements. The criterion isn't used very frequently, but it is of theoretical importance for some applications. Proceed to [[Guided tour for beginners:Manipulating equations in groups]] OR Return to [[Guided tour for beginners:Subsemigroup of finite group is subgroup]]}}
-==Statement==
+{{#lst:Sufficiency of subgroup criterion|main}}

Vipul: 5 revisions

2008-05-07T23:40:58Z

5 revisions

← Older revision	Revision as of 23:40, 7 May 2008
(No difference)

Vipul at 19:41, 22 March 2008

2008-03-22T19:41:25Z

← Older revision		Revision as of 19:41, 22 March 2008
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	__NOTOC__		__NOTOC__
			{{derivative of\|sufficiency of subgroup condition}}
	{{guided tour\|beginners\|Introduction two\|Manipulating equations in groups\|Subsemigroup of finite group is subgroup}}		{{guided tour\|beginners\|Introduction two\|Manipulating equations in groups\|Subsemigroup of finite group is subgroup}}
	{{quotation\|This is a general condition for a nonempty subset to be a subgroup. We only check for left quotients of elements. The criterion isn't used very frequently, but it is of theoretical importance for some applications. Proceed to [[Guided tour for beginners:Manipulating equations in groups]] OR Return to [[Guided tour for beginners:Subsemigroup of finite group is subgroup]]}}		{{quotation\|This is a general condition for a nonempty subset to be a subgroup. We only check for left quotients of elements. The criterion isn't used very frequently, but it is of theoretical importance for some applications. Proceed to [[Guided tour for beginners:Manipulating equations in groups]] OR Return to [[Guided tour for beginners:Subsemigroup of finite group is subgroup]]}}

Vipul at 16:55, 22 March 2008

2008-03-22T16:55:27Z

← Older revision		Revision as of 16:55, 22 March 2008
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	{{guided tour\|beginners}}		__NOTOC__
			{{guided tour\|beginners\|Introduction two\|Manipulating equations in groups\|Subsemigroup of finite group is subgroup}}
	{{quotation\|This is a general condition for a nonempty subset to be a subgroup. We only check for left quotients of elements. The criterion isn't used very frequently, but it is of theoretical importance for some applications. Proceed to [[Guided tour for beginners:Manipulating equations in groups]] OR Return to [[Guided tour for beginners:Subsemigroup of finite group is subgroup]]}}		{{quotation\|This is a general condition for a nonempty subset to be a subgroup. We only check for left quotients of elements. The criterion isn't used very frequently, but it is of theoretical importance for some applications. Proceed to [[Guided tour for beginners:Manipulating equations in groups]] OR Return to [[Guided tour for beginners:Subsemigroup of finite group is subgroup]]}}
	==Statement==		==Statement==

Vipul at 12:20, 22 March 2008

2008-03-22T12:20:54Z

← Older revision		Revision as of 12:20, 22 March 2008
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	{{quotation\|This is a general condition for a nonempty subset to be a subgroup. We only check for left quotients of elements. The criterion isn't used very frequently, but it is of theoretical importance for some applications. Proceed to [[Guided tour for beginners:~~Factsheet two~~]] OR Return to [[Guided tour for beginners:Subsemigroup of finite group is subgroup]]}}		{{guided tour\|beginners}}
			{{quotation\|This is a general condition for a nonempty subset to be a subgroup. We only check for left quotients of elements. The criterion isn't used very frequently, but it is of theoretical importance for some applications. Proceed to [[Guided tour for beginners:Manipulating equations in groups]] OR Return to [[Guided tour for beginners:Subsemigroup of finite group is subgroup]]}}
	==Statement==		==Statement==

Vipul at 22:51, 21 March 2008

2008-03-21T22:51:16Z

← Older revision		Revision as of 22:51, 21 March 2008
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	{{quotation\|This is a general condition for a nonempty subset to be a subgroup. We only check for left quotients of elements. The criterion isn't used very frequently, but it is of theoretical importance for some applications. Return to [[Guided tour for beginners:Subsemigroup of finite group is subgroup]]}}		{{quotation\|This is a general condition for a nonempty subset to be a subgroup. We only check for left quotients of elements. The criterion isn't used very frequently, but it is of theoretical importance for some applications. Proceed to [[Guided tour for beginners:Factsheet two]] OR Return to [[Guided tour for beginners:Subsemigroup of finite group is subgroup]]}}
	==Statement==		==Statement==