73.114 ActorSquareRecord

ActorSquareRecord( X )

ActorSquareRecord( C )

This function creates a new field .actorSquare for the crossed module or cat1-group, initially containing .isActorSquare := true and .xmod or .cat1 as appropriate. Components for the actor of X or C are stored here when constructed.

    gap> ActorSquareRecord( X1 );
    rec(
      isActorSquare := true,
      xmod := Crossed module [c5->PermAut(c5)],
      WhiteheadPermGroup := WG([c5->PermAut(c5)]),
      automorphismPermGroup := PermAut([c5->PermAut(c5)]),
      Whitehead := Crossed module Whitehead[c5->PermAut(c5)],
      Norrie := Crossed module Norrie[c5->PermAut(c5)],
      Lue := Crossed module Lue[c5->PermAut(c5)],
      actor := Crossed module Actor[c5->PermAut(c5)],
      innerMorphism :=  Morphism of crossed modules
          <[c5->PermAut(c5)] >-> Actor[c5->PermAut(c5)]>,
      innerActor := Crossed module Actor[c5->PermAut(c5)] )  

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