Supernormal subhypergroup - Revision history

Vipul at 20:04, 24 August 2008

2008-08-24T20:04:01Z

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	{{subhypergroup property}}		{{subhypergroup property}}

	{{analogue ~~in-~~of\|hypergroup\|subgroup~~\|normality~~}}		{{analogue of property\|
			old generic context = group\|
			old specific context = subgroup\|
			new generic context = hypergroup\|
			new specific context = subhypergroup\|
			old property = normal subgroup}}

	==History==		==History==

Vipul: 7 revisions

2008-05-08T00:24:23Z

7 revisions

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Vipul at 00:01, 27 April 2008

2008-04-27T00:01:19Z

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	==History==		==History==

Vipul at 23:26, 10 March 2008

2008-03-10T23:26:24Z

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Vipul at 08:02, 13 June 2007

2007-06-13T08:02:19Z

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Vipul at 08:02, 13 June 2007

2007-06-13T08:02:01Z

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Vipul: /* Origin */

2007-06-12T21:48:51Z

Origin

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	===Origin===		===Origin===

	The term ''supernormal subhypergroup''' was introduced by Bloom and Heyer in their paper ''Cpnvergence of convolution products of probability measures on hypergroups''.		The term ''supernormal subhypergroup'' was introduced by Bloom and Heyer in their paper ''Cpnvergence of convolution products of probability measures on hypergroups''.

	==Definition==		==Definition==

Vipul at 21:48, 12 June 2007

2007-06-12T21:48:28Z

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 {{hypergroup analogue of|normality}}
 ==Definition==
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 * [[Normal subhypergroup]]

Vipul at 21:39, 12 June 2007

2007-06-12T21:39:05Z

New page

{{subhypergroup property}}

{{hypergroup analogue of|normality}}

==Definition==

A [[subhypergroup]] <math>H</math> of a [[hypergroup]] <math>K</math> is said to be '''supernormal''' if <math>x * H * \overline{x} = H</math> for every element <math>x \in K</math>.

==Analogy==

The subhypergroup property of being supernormal is analogous to the subgroup property of being normal, as per the following definition: a [[subgroup]] <math>H</math> of a [[group]]<math>K</math> is said to be [[normal subgroup|normal]] if <math>xHx^{-1} = H</math> for any <math>x \in K</math>.

==Relation with other properties==

===Weaker properties===

* [[Normal subhypergroup]]