GAP:SylowComplement

Function type
This function takes as input two arguments, the first representing a group and the second being a prime number. It returns a group.

Behavior

 * The function takes as input a finite solvable group $$G$$ and a prime number $$p$$ and outputs a $$p'$$-Hall subgroup, or a $$p$$-Sylow complement.
 * If the first argument is a group but is not finite or solvable, the function returns a NoMethodFound error.
 * If the first argument is not a group, GAP returns a NoMethodFound error.

Related functions

 * GAP:SylowSubgroup
 * GAP:HallSubgroup

Examples of usage
gap> SylowComplement(SymmetricGroup(4),2); Group([ (2,4,3) ]) gap> SylowComplement(SymmetricGroup(5),2); Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 3rd choice method found for `SylowComplementOp' on 2 arguments calle\ d from  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