GAP:CyclicGroup

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([, ]n)

where $$n$$ is a positive integer. Here are the possibilities:

Related functions

 * DihedralGroup
 * SymmetricGroup
 * AlternatingGroup

Examples of usage
gap> G := CyclicGroup(5);  gap> H := CyclicGroup(8);  gap> Subgroups(H); [ Group([ 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 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>