73.95 AllSections

AllSections( C [,"endo" rm or "xmod"] )

By default, this function computes the set of idempotent endomorphisms from R to R (see sections refEndomorphismClasses, refIdempotentImages) and takes these as possible choices for the composite homomorphism hxi. A backtrack procedure then calculates possible images for such a section. This function calculates all the sections of {cal C} and overwrites any existing subfields of C.sections.

    gap> allSC := AllSections( SC );
    AllSections record for cat1-group [c3^2

Xc2 ==> s3],
    : 6 regular sections,  3 irregular ones found. 
    gap> RecFields( allSC );
    [ "areSections", "isReg", "isAll", "regular", "genimageList",
      "generators", "cat1", "operations" ]
    gap> PrintList( allSC.genimageList );
    [ ( 4, 5, 6), ( 2, 3)( 5, 6) ]
    [ ( 4, 5, 6), ( 1, 3)( 4, 5) ]
    [ ( 4, 5, 6), ( 1, 2)( 4, 6) ]
    [ ( 1, 3, 2)( 4, 6, 5), ( 2, 3)( 5, 6) ]
    [ ( 1, 3, 2)( 4, 6, 5), ( 1, 3)( 4, 5) ]
    [ ( 1, 3, 2)( 4, 6, 5), ( 1, 2)( 4, 6) ]
    [ ( 1, 2, 3), ( 2, 3)( 5, 6) ]
    [ ( 1, 2, 3), ( 1, 2)( 4, 6) ]
    [ ( 1, 2, 3), ( 1, 3)( 4, 5) ] 
    gap> allXSC := AllDerivations( XSC, "cat1" );
    AllDerivations record for crossed module [c3->s3],
    : 6 regular derivations,  3 irregular ones found.   

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