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