GAP:DihedralGroup
From Groupprops
This article is about a GAP function.
Definition
Function type
The function takes as input a positive integer (supposed to be even) and outputs a group. An optional filter can be provided.
Behavior
The function is invoked by:
DihedralGroup([<filt>, ]n)
where is a positive integer. Here are the possibilities:
Nature of input | Output |
---|---|
No filter, an even integer | constructs the dihedral group of order , degree as a PcGroup (i.e., the group is stored in terms of a polycyclic series). The output confirms this |
Filter chosen as IsPermGroup, an even integer | the dihedral group of order is constructed as a permutation group on letters (note: this is not the same as the default permutation action on letters) |
something other than an even integer | NoMethodFound error |
Related facts
Examples of usage
gap> G := DihedralGroup(8); <pc group of size 8 with 3 generators> gap> IdGroup(G); [ 8, 3 ] gap> H := DihedralGroup(16); <pc group of size 16 with 4 generators> gap> IsSubgroup(H,G); false gap> IsPcGroup(H); true gap> K := DihedralGroup(IsPermGroup,10); Group([ (1,2,3,4,5), (2,5)(3,4) ]) gap> Order(K); 10 gap> L := DihedralGroup(31); Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 2nd choice method found for `DihedralGroupCons' on 2 arguments called from DihedralGroupCons( IsPcGroup, arg[1] ) called from <function>( <arguments> ) called from read-eval-loop Entering break read-eval-print loop ... you can 'quit;' to quit to outer loop, or you can 'return;' to continue