73.41 Kernel of a crossed module morphism

Kernel( mor )

The kernel of a morphism mor : X to Y of crossed modules is the normal sub-crossed module of X whose source is the kernel of mor.sourceHom and whose range is the kernel of mor.rangeHom. An appropriate name for the kernel is chosen automatically. A field .kernel is added to mor.

    gap> XModMorphismName( mor );;
    gap> KX := Kernel( mor );
    Crossed module Ker<[q8->sl(2,3)] >-> [k4->a4]>
    gap> XModPrint( KX );
    Crossed module Ker<[q8->SL(2,3)] >-> [k4->a4]> :- 
    : Source group has parent ( sl(2,3) )  and has generators:
      [ (1,3)(2,4)(5,7)(6,8) ]
    : Range group has parent ( sl(2,3) )  and has generators:
      [ ( 1, 3)( 2, 4)( 5, 7)( 6, 8) ]
    : Boundary homomorphism maps source generators to:
      [ (1,3)(2,4)(5,7)(6,8) ]
    : The automorphism group is trivial.
    gap> IsNormalSubXMod( SX, KX );
    true   

Previous Up Top Next
Index