73.13 RModuleXMod

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.

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GAP 3.4.4
April 1997