73.35 SubXMod

SubXMod( X, subS, subR )

A sub-crossed module of a crossed module X has as source a subgroup subS of X.source and as range a subgroup subR of X.range. The boundary map and the action are the appropriate restrictions. In the following example we construct a sub-crossed module of SX with range q8 and source a cyclic group of order 4.

    gap> q8 := SX.source;; genq8 := q8.generators;;
    gap> q8.name := "q8";; XModName( SX );;
    gap> c4 := Subgroup( q8, [ genq8[1] ] );
    Subgroup( sl(2,3), [ (1,2,3,4)(5,8,7,6) ] )
    gap> c4.name := "c4";;
    gap> subSX := SubXMod( SX, c4, q8 );
    Crossed module [c4->q8] 
    gap> XModPrint( subSX );
    Crossed module [c4->q8] :- 
    : Source group has parent ( sl(2,3) ) and has generators:
      [ (1,2,3,4)(5,8,7,6) ]
    : Range group has parent ( sl(2,3) ) and has generators:
      [ (1,2,3,4)(5,8,7,6), ( 1, 5, 3, 7)( 2, 6, 4, 8) ]
    : Boundary homomorphism maps source generators to:
      [ ( 1, 2, 3, 4)( 5, 8, 7, 6) ]
    : Action homomorphism maps range generators to automorphisms:
      (1,2,3,4)(5,8,7,6) --> {source gens --> [ (1,2,3,4)(5,8,7,6) ]}
      (1,5,3,7)(2,6,4,8) --> {source gens --> [ (1,4,3,2)(5,6,7,8) ]}
      These 2 automorphisms generate the group of automorphisms.  

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GAP 3.4.4
April 1997