GAP:SylowComplement

This article is about a GAP function.

Definition

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

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
<compiled or corrupted call value>  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