Normal not implies strongly potentially characteristic - Revision history

Vipul at 18:47, 30 May 2009

2009-05-30T18:47:07Z

← Older revision		Revision as of 18:47, 30 May 2009
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	{{subgroup property non-implication\|		{{subgroup property non-implication\|
	stronger = normal subgroup\|		stronger = normal subgroup\|
	weaker = ~~strongly~~ potentially characteristic subgroup}}		weaker = characteristic-potentially characteristic subgroup}}

	==Statement==		==Statement==
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	===Verbal statement===		===Verbal statement===

	A [[normal subgroup]] need not be [[~~strongly~~ potentially characteristic subgroup\|~~strongly~~ potentially characteristic]].		A [[normal subgroup]] need not be [[characteristic-potentially characteristic subgroup\|characteristic-potentially characteristic]].

	===Statement with symbols===		===Statement with symbols===
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	==Facts used==		==Facts used==

	# [[uses::~~Strongly~~ potentially characteristic implies ~~semi~~-~~strongly~~ potentially characteristic]]		# [[uses::Characteristic-potentially characteristic implies normal-potentially characteristic]]
	# [[uses::Normal not implies ~~semi~~-~~strongly~~ potentially characteristic]]		# [[uses::Normal not implies normal-potentially characteristic]]

	==Proof==		==Proof==

	The proof follows directly from facts (1) and (2).		The proof follows directly from facts (1) and (2).

Vipul: /* Verbal statement= */

2009-04-23T12:58:01Z

Verbal statement=

← Older revision		Revision as of 12:58, 23 April 2009
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	==Statement==		==Statement==

	==Verbal statement===		===Verbal statement===

	A [[normal subgroup]] need not be [[strongly potentially characteristic subgroup\|strongly potentially characteristic]].		A [[normal subgroup]] need not be [[strongly potentially characteristic subgroup\|strongly potentially characteristic]].

Vipul: Created page with '{{subgroup property non-implication| stronger = normal subgroup| weaker = strongly potentially characteristic subgroup}} ==Statement== ==Verbal statement=== A [[normal subgrou...'

2009-04-23T12:57:39Z

Created page with '{{subgroup property non-implication| stronger = normal subgroup| weaker = strongly potentially characteristic subgroup}} ==Statement== ==Verbal statement=== A [[normal subgrou...'

New page

{{subgroup property non-implication|
stronger = normal subgroup|
weaker = strongly potentially characteristic subgroup}}

==Statement==

==Verbal statement===

A [[normal subgroup]] need not be [[strongly potentially characteristic subgroup|strongly potentially characteristic]].

===Statement with symbols===

It is possible to have a [[group]] <math>K</math> and a [[normal subgroup]] <math>H</math> of <math>K</math> such that there is no group <math>G</math> containing <math>K</math> in which both <math>H</math> and <math>K</math> are [[characteristic subgroup]]s.

==Facts used==

# [[uses::Strongly potentially characteristic implies semi-strongly potentially characteristic]]
# [[uses::Normal not implies semi-strongly potentially characteristic]]

==Proof==

The proof follows directly from facts (1) and (2).