73.116 Whitehead crossed module

Whitehead( X )

This crossed module has the source of X as source, and the Whitehead group WX as range. The boundary maps each element to the inner derivation which it defines. The action uses SourceEndomorphismDerivation.

    gap> WXSC := Whitehead( XSC );
    Crossed module Whitehead[c3->s3]
    gap> XModPrint( WXSC );
    Crossed module Whitehead[c3->s3] :- 
    : Source group has parent ( c3^2

Xc2 ) and has generators:
      [ (1,2,3)(4,6,5) ]
    : Range group = WG([c3->s3]) has generators:
      [ (1,2,3)(4,6,5), (1,4)(2,5)(3,6) ]
    : Boundary homomorphism maps source generators to:
      [ (1,3,2)(4,5,6) ]
    : Action homomorphism maps range generators to automorphisms:
      (1,2,3)(4,6,5) --> { source gens --> [ (1,2,3)(4,6,5) ] }
      (1,4)(2,5)(3,6) --> { source gens --> [ (1,3,2)(4,5,6) ] }
      These 2 automorphisms generate the group of automorphisms.  

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