73.48 Cat1

Cat1( G, t, h )

This function constructs a cat1-group {cal C} from a group G and a pair of endomorphisms, the tail and head of {cal C}. The example uses the holomorph of c5, a group of size 20, which was the source group in XC1 in refAbout cat1-groups. Note that when t = h the boundary is the zero map.

    gap> h20 := Group( (1,2,3,4,5), (2,3,5,4) );;
    gap> h20.name := "h20";;
    gap> genh20 := h20.generators;;
    gap> imh20 := [ (), (2,3,5,4) ];;
    gap> h := GroupHomomorphismByImages( h20, h20, genh20, imh20 );;
    gap> t := h;;
    gap> C := Cat1( h20, t, h );
    cat1-group [h20 ==> R]