GAP:CyclicGroup
From Groupprops
This article is about a GAP function.
Definition
Function type
The function takes as input a positive integer and outputs a group. An optional filter can be provided that controls the form in which the group is constructed and stored.
Behavior
The function is invoked by:
CyclicGroup([<filt>, ]n)
where is a positive integer. Here are the possibilities:
Nature of input | Output |
---|---|
No filter, ![]() |
cyclic group (specifically, finite cyclic group) of order ![]() |
IsPermGroup as filter, ![]() |
cyclic group of order ![]() ![]() ![]() |
IsMatrixGroup as filter, ![]() |
cyclic group of order ![]() |
Related functions
Examples of usage
gap> G := CyclicGroup(5); <pc group of size 5 with 1 generators> gap> H := CyclicGroup(8); <pc group of size 8 with 3 generators> gap> Subgroups(H); [ Group([ <identity> of ... ]), Group([ f3 ]), Group([ f2 ]), Group([ f1, f2, f3 ]) ] gap> K := CyclicGroup(IsPermGroup,9); Group([ (1,2,3,4,5,6,7,8,9) ]) gap> L := CyclicGroup(IsMatrixGroup,3); Group([ [ [ 0, 1, 0 ], [ 0, 0, 1 ], [ 1, 0, 0 ] ] ]) gap> Set(L); [ [ [ 0, 0, 1 ], [ 1, 0, 0 ], [ 0, 1, 0 ] ], [ [ 0, 1, 0 ], [ 0, 0, 1 ], [ 1, 0, 0 ] ], [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] ] gap> CyclicGroup(0); Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `CyclicGroupCons' on 2 arguments called from CyclicGroupCons( 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 brk>