GAP:OrderStatisticsCumulative

Definition

Function type

The function takes as input a finite group.

Behavior

The function outputs the cumulative order statistics of the group. It gives, as a list sorted by increasing order of divisors of the order, the number of elements of the group whose order divides that number.

Method

Code

OrderStatisticsCumulative := function(G)
        local L,D;
        L := List(Set(G),Order);
        D := DivisorsInt(Order(G));
        return(List(D,x->Length(Filtered(L,y->x mod y = 0))));
end;;

Here is the paired version, that pairs a divisor and the number of elements whose order divides that divisor:

OrderStatisticsCumulativePaired := function(G)
        local L,D;
        L := List(Set(G),Order);
        D := DivisorsInt(Order(G));
        return(List(D,x->[x,Length(Filtered(L,y->x mod y = 0))]));
end;;