GAP:StructureDescription - Revision history

Vipul at 20:03, 20 June 2011

2011-06-20T20:03:52Z

← Older revision		Revision as of 20:03, 20 June 2011
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	\| a finite group that GAP can recognize \|\| a string giving a description of the group \|\| <tt>StructureDescription(SmallGroup(24,8))</tt> gives <tt>"(C6 x C2) : C2"</tt><br><tt> StructureDescription(SmallGroup(16,8))</tt> gives <tt>"QD16"</tt>\|\| Isomorphic groups ''always'' give the same structure description. However, it is possible to have non-isomorphic groups that give the same structure description.		\| a finite group that GAP can recognize \|\| a string giving a description of the group \|\| <tt>StructureDescription(SmallGroup(24,8))</tt> gives <tt>"(C6 x C2) : C2"</tt><br><tt> StructureDescription(SmallGroup(16,8))</tt> gives <tt>"QD16"</tt>\|\| Isomorphic groups ''always'' give the same structure description. However, it is possible to have non-isomorphic groups that give the same structure description.
	\|-		\|-
	\| an infinite group or some other input \|\| a [[GAP:NoMethodFound\|NoMethodFound]]] error \|\| \|\|		\| an infinite group or some other input \|\| a [[GAP:NoMethodFound\|NoMethodFound]] error \|\| \|\|
	\|}		\|}

Vipul at 20:03, 20 June 2011

2011-06-20T20:03:40Z

← Older revision		Revision as of 20:03, 20 June 2011
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	! Nature of input !! Output !! Example inputs and corresponding outputs !! Additional comments		! Nature of input !! Output !! Example inputs and corresponding outputs !! Additional comments
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	\| a finite group that GAP can recognize \|\| a string giving a description of the group \|\| <tt>StructureDescription(SmallGroup(24,8))</tt> gives <tt>"(C6 x C2) : C2"</tt><br><tt> StructureDescription~~(AutomorphismGroup~~(SmallGroup(16,7)));</tt> gives <tt>"~~(C2 x D8) : C2~~"</tt>\|\| Isomorphic groups ''always'' give the same structure description. However, it is possible to have non-isomorphic groups that give the same structure description.		\| a finite group that GAP can recognize \|\| a string giving a description of the group \|\| <tt>StructureDescription(SmallGroup(24,8))</tt> gives <tt>"(C6 x C2) : C2"</tt><br><tt> StructureDescription(SmallGroup(16,8))</tt> gives <tt>"QD16"</tt>\|\| Isomorphic groups ''always'' give the same structure description. However, it is possible to have non-isomorphic groups that give the same structure description.
	\|-		\|-
	\| an infinite group or some other input \|\| a [[GAP:NoMethodFound\|NoMethodFound]]] error \|\|		\| an infinite group or some other input \|\| a [[GAP:NoMethodFound\|NoMethodFound]]] error \|\| \|\|
	\|}		\|}

Vipul: Created page with "{{GAP function}} ==Definition== ===Function type=== This function takes as input a group and outputs a string that gives quick description of the group's structure. ===Behavi..."

2011-06-20T20:03:03Z

Created page with "{{GAP function}} ==Definition== ===Function type=== This function takes as input a group and outputs a string that gives quick description of the group's structure. ===Behavi..."

New page

{{GAP function}}

==Definition==

===Function type===

This function takes as input a group and outputs a string that gives quick description of the group's structure.

===Behavior===

{| class="sortable" border="1"
! Nature of input !! Output !! Example inputs and corresponding outputs !! Additional comments
|-
| a finite group that GAP can recognize || a string giving a description of the group || <tt>StructureDescription(SmallGroup(24,8))</tt> gives <tt>"(C6 x C2) : C2"</tt><br><tt> StructureDescription(AutomorphismGroup(SmallGroup(16,7)));</tt> gives <tt>"(C2 x D8) : C2"</tt>|| Isomorphic groups ''always'' give the same structure description. However, it is possible to have non-isomorphic groups that give the same structure description.
|-
| an infinite group or some other input || a [[GAP:NoMethodFound|NoMethodFound]]] error ||
|}

==Aspects of structure description==

===Basic constructions===

{| class="sortable" border="1"
! Letter/symbol !! Number of parameters !! Interpretation !! Example
|-
| 1 || 0 || [[trivial group]] ||
|-
| C || 1 for size || [[cyclic group]] of size equal to the parameter || "C8" stands for the [[cyclic group:Z8|cyclic group of order eight]].
|-
| A || 1 for degree || [[alternating group]] of degree equal to the parameter || "A5" stands for the [[alternating group:A5|alternating group of degree five]].
|-
| S || 1 for degree || [[symmetric group]] of degree equal to the parameter || "S4" stands for the [[symmetric group:S4|symmetric group of degree four]].
|-
| D || 1 for order || [[dihedral group]] of order equal to the parameter. Note that the order is twice the ''degree'' || "D8" stands for the [[dihedral group:D8|dihedral group of order eight]].
|-
| Q || 1 for order || [[generalized quaternion group]] of order equal to the parameter. || "Q16" stands for [[generalized quaternion group:Q16]]
|-
| QD || 1 for order || quasidihedral group (called [[semidihedral group]] on this wiki) of order equal to the parameter. || "QD16" stands for [[semidihedral group:SD16]]
|-
| PSL || 2: 1 for degree (order of matrices), 1 for size of field || [[projective special linear group]] of given degree over field of given size || "PSL(2,11)" stands for [[projective special linear group:PSL(2,11)]]: the [[projective special linear group of degree two]] over [[field:F11]].
|-
| SL || 2: 1 for degree (order of matrices), 1 for size of field || [[special linear group]] of given degree over field of given size || "SL(2,5)" stands for [[special linear group:SL(2,5)]]: the [[special linear group of degree two]] over [[field:F5]].
|-
| GL || 2: 1 for degree (order of matrices), 1 for size of field || ||
|}

''The table needs to be completed''

===Combination constructions===

{{fillin}}

===Precedence rules in case of multiple descriptions===