RModuleXMod( Rmod )
The crossed module RX obtained from an R-module has the abelian
group M as source, the zero map as boundary, the group R which
acts on M as range, the group A of automorphisms of M as
RX.aut and alpha : R to A as RX.action. An appropriate name
for RX is chosen automatically. Continuing the previous example,
M is k4 and R is cyclic of order 3.
gap> RX := RModuleXMod( R );
Crossed module [v4->PermSubAut(v4)]
gap> XModPrint( RX );
Crossed module [v4->PermSubAut(v4)]
: Source group has parent s4 and has generators:
[ (1,2)(3,4), (1,3)(2,4) ]
: Range group = PermSubAut(v4) has generators:
[ (1,2,3) ]
: Boundary homomorphism maps source generators to:
[ () ]
: Action homomorphism maps range generators to automorphisms:
(1,2,3) --> { source gens --> [ (1,3)(2,4), (1,4)(2,3) ] }
This automorphism generates the group of automorphisms.
GAP 3.4.4