Hi,
How about running the following program:
n:=90; # try with other values
i:=0;
Print("GROUP ORDER is ", " ", n, "\n");
g:= AllSmallGroups(n);
for xx in g do
i:=i+1;
Print( "\n", "SMALL GROUP", "(" , n, "," , i, ") =
",StructureDescription(xx), "\n","\n");
yy:= Set(List(xx,Order));
for y in yy do
zz:= Number(xx, x -> Order(x)=y);
Print("order = ", y, " ", "number of elts = ", zz, "\n", "\n"); od;
od;
Ashish Kumar Das
Maths Dept.
NEHU, Shillong, INDIA
On 1/7/11, Vipul Naik <vi...@math.uchicago.edu> wrote:
> Hi,
>
> If I understand your question correctly, you want information on how
> many elements of a finite group have each possible order. Although I
> don't think there are built-in functions for this, it is easy to write
> code for these. For instance:
>
> OrderStatisticsPaired := function(G)
> local L,D;
> L := List(Set(G),Order);
> D := DivisorsInt(Order(G));
> return(List(D,x->[x,Length(Filtered(L,y->x=y))]));
> end;;
>
> This function takes as input a group and gives a list of ordered
> pairs, for each divisor of the order of the group, how many elements
> of the group have that order. For instance:
>
> OrderStatisticsPaired(SymmetricGroup(4))
>
> gives the output:
>
> [ [ 1, 1 ], [ 2, 9 ], [ 3, 8 ], [ 4, 6 ], [ 6, 0 ], [ 8, 0 ], [ 12, 0 ], [
> 24, 0 ] ]
>
> indicating that in the symmetric group on four letters, there is one
> element of the group of order one, nine elements of order two, eight
> elements of order three, six elements of order four, and no element of
> any higher order.
>
> This exact function may not suit your needs but it's likely that some
> variant of it will.
>
> This code is inefficient for large groups; for such groups, one can
> modify the code to only go over conjugacy classes instead of elements.
>
> To create such a function, you can either paste the function code in
> front of the GAP command prompt or include this in a file and then use
> GAP's "Read" command to read that file in.
>
> Vipul
>
> * Quoting Sara Radfar who at 2011-01-06 05:14:32+0000 (Thu) wrote
>> Hi
>>
>> I can find the same order elements of a group but can't find the set
>> of the number of the same order elements of a group.Also how we can
>> introduce a sporadic simple group to GAP?.For example $CO$.
>>
>> Thanks
>> Sara
>>
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