66.8 Properties of Tables of Marks

For a table of marks tom of a group G, the following properties have the same meaning as the corresponding properties for G. Additionally, if a positive integer sub is given as the second argument then the value of the corresponding property for the sub-th class of subgroups of tom is returned.

IsAbelianTom( tom[, sub] )indexttIsAbelianTom

IsCyclicTom( tom[, sub] )indexttIsCyclicTom

IsNilpotentTom( tom[, sub] )indexttIsNilpotentTom

IsPerfectTom( tom[, sub] )indexttIsPerfectTom

IsSolvableTom( tom[, sub] )indexttIsSolvableTom

gap> tom:= TableOfMarks( "A5" );;
gap> IsAbelianTom( tom );  IsPerfectTom( tom );
false
true
gap> IsAbelianTom( tom, 3 );  IsNilpotentTom( tom, 7 );
true
false
gap> IsPerfectTom( tom, 7 );  IsSolvableTom( tom, 7 );
false
true
gap> for i in [ 1 .. 6 ] do
> Print( i, ": ", IsCyclicTom(a5, i), "  " );
> od;  Print( "\n" );
1: true  2: true  3: true  4: false  5: true  6: false

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