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.
GAP 3.4.4