73.126 Actor for cat1-groups

Actor( C )

The actor of a cat1-group {cal C} is the cat1-group associated to the actor crossed module of the crossed module {cal X} associated to {cal C}. Its range is the automorphism group A and its source is A semidirect W where W is the Whitehead group.

    gap> ActSC := Actor( SC );;
    gap> Cat1Print( ActSC );
    cat1-group Actor[c3^2
|
Xc2 ==> s3] :- 
    : source group has generators:
      [ (4,6,5), (2,3)(5,6), (1,2,3)(4,6,5), (1,4)(2,5)(3,6) ]
    :  range group has generators:
      [ (5,6,7), (1,2)(3,4)(6,7) ]
    : tail homomorphism maps source generators to:
      [ (5,6,7), (1,2)(3,4)(6,7), (), () ]
    : head homomorphism maps source generators to:
      [ (5,6,7), (1,2)(3,4)(6,7), (5,7,6), (1,2)(3,4)(6,7) ]
    : range embedding maps range generators to:
      [ (4,6,5), (2,3)(5,6) ]
    : kernel has generators:
      [ (1,2,3)(4,6,5), (1,4)(2,5)(3,6) ]
    : boundary homomorphism maps generators of kernel to:
      [ (5,7,6), (1,2)(3,4)(6,7) ]
    : kernel embedding maps generators of kernel to:
      [ (1,2,3)(4,6,5), (1,4)(2,5)(3,6) ]
    : associated crossed module is Crossed module Actor[c3->s3]  

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GAP 3.4.4
April 1997