Element enumeration - Revision history

Vipul: 3 revisions

2008-05-07T23:27:07Z

3 revisions

← Older revision	Revision as of 23:27, 7 May 2008
(No difference)

Vipul: /* Stronger subgroup description rules */

2008-01-02T22:34:28Z

Stronger subgroup description rules

← Older revision		Revision as of 22:34, 2 January 2008
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	===Stronger subgroup description rules===		===Stronger subgroup description rules===

	* [[Generating set]] gives an element enumeration if we consider all the generators, all the products of length two of generators and so on.		* [[Generating set (subgroup description)\|generating set]] gives an element enumeration if we consider all the generators, all the products of length two of generators and so on.
	* [[Membership test]] uses an element enumeration of the whole group to obtain an element enumeration of the subgroup, by ''filtering'' in only those elements which are in the subgroup		* [[Membership test]] uses an element enumeration of the whole group to obtain an element enumeration of the subgroup, by ''filtering'' in only those elements which are in the subgroup

Vipul: /* Relation with other subgroup description rules */

2008-01-02T22:33:36Z

Relation with other subgroup description rules

← Older revision		Revision as of 22:33, 2 January 2008
Line 20:		Line 20:
	* [[Generating set]] gives an element enumeration if we consider all the generators, all the products of length two of generators and so on.		* [[Generating set]] gives an element enumeration if we consider all the generators, all the products of length two of generators and so on.
	* [[Membership test]] uses an element enumeration of the whole group to obtain an element enumeration of the subgroup, by ''filtering'' in only those elements which are in the subgroup		* [[Membership test]] uses an element enumeration of the whole group to obtain an element enumeration of the subgroup, by ''filtering'' in only those elements which are in the subgroup

			==Effect of subgroup operators==

			{{join-closed sdr}}

Vipul at 23:57, 21 April 2007

2007-04-21T23:57:09Z

New page

{{subgroup description rule}}

==Definition==

{{subgroup-description setup}}

===Definition part===

An '''element enumeration''' for <math>H</math> is an algorithm that outputs a sequence of elements of <math>G</math> such that:

* Every element in the sequence lies inside <math>H</math>
* The sequence contains every element of <math>H</math>

Note that because of repetitions of elements, the enumeration may itself be much longer and take more time to compute than the size of <math>H</math>.

==Relation with other subgroup description rules==

===Stronger subgroup description rules===

* [[Generating set]] gives an element enumeration if we consider all the generators, all the products of length two of generators and so on.
* [[Membership test]] uses an element enumeration of the whole group to obtain an element enumeration of the subgroup, by ''filtering'' in only those elements which are in the subgroup