73.73 SubCat1

SubCat1( C, H )

When H is a subgroup of C.source and the restrictions of C.tail and C.head to H have a common image, these homomorphisms determine a sub-cat1-group of C.

    gap> d20 := Subgroup( h20, [ (1,2,3,4,5), (2,5)(3,4) ] );;
    gap> subC := SubCat1( C, d20 );
    cat1-group [Sub[h20 ==> c4]] 
    gap> Cat1Print( subC );

    cat1-group [Sub[h20 ==> c4]] :- 
    : source group has generators:
      [ (1,2,3,4,5), (2,5)(3,4) ]
    :  range group has generators:
      [ ( 2, 5)( 3, 4) ]
    : tail homomorphism maps source generators to:
      [ (), ( 2, 5)( 3, 4) ]
    : head homomorphism maps source generators to:
      [ (), ( 2, 5)( 3, 4) ]
    : range embedding maps range generators to:
      [ ( 2, 5)( 3, 4) ]
    : kernel has generators:
      [ (1,2,3,4,5) ]
    : boundary homomorphism maps generators of kernel to:
      [ () ]
    : kernel embedding maps generators of kernel to:
      [ ( 1, 2, 3, 4, 5) ]   

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