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.
GAP 3.4.4