# Problem using GAP Anonymous

Hello,

I'm starting to use the GAP package/software with the follow commands to define a simple finite group:

gap> f := FreeGroup("x");

<free group="" on="" the="" generators="" [="" x="" ]&gt;<="" p="">

gap> AssignGeneratorVariables(f);

I Assigned the global variables [ x ]

gap> x^5 * x^-7;

x^-2

gap> g := f/[x^5];

<fp group="" on="" the="" generators="" [x]&gt;<="" p="">

gap> AssignGeneratorVariables(g);

I Global Variable x already defined and will be overwritten I Assigned the global variables [ x ]

gap> Size(g);

5

gap> List(g);

Here is the problem, I should get:

[ identity ..., x, x^2, x^3, x^4 ]

[ identity ..., x, x^-1, x^2, x^-2 ]

1) What am I doing wrong, please?

Also, the command:

gap> MultTable(g);

Error, Variable: 'MultTable' must have a value not in any function at line 8 of stdin

Can someone please help with that? I have a lot of ideas on Group / Abstract Algebra but despite I use/read the GAP manual I can't create a simple multiplication table.

Any hint/help will be appreciate.

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Regarding your first problem: in the group you defined, x^-1 is the same as x^4, and x^-2 is the same as x^3, so the answer returned by GAP is correct. I don't know if there is a way to ask GAP to display only positive powers.

As for the multiplication table, you need to spell it MultiplicationTable instead of MultTable:

gap> f := FreeGroup("x");
<free group on the generators [ x ]>
gap> AssignGeneratorVariables(f);
#I  Assigned the global variables [ x ]
gap> x^5 * x^-7;
x^-2
gap> g := f/[x^5];
<fp group on the generators [ x ]>
gap> AssignGeneratorVariables(g);
#I  Global variable x' is already defined and will be overwritten
#I  Assigned the global variables [ x ]
gap> Size(g);
5
gap> List(g);
[ <identity ...>, x, x^-1, x^2, x^-2 ]
gap> MultTable(g);
Error, Variable: 'MultTable' must have a value
not in any function at line 16 of *stdin*
gap> MultiplicationTable(g);
[ [ 1, 2, 3, 4, 5 ], [ 2, 3, 4, 5, 1 ], [ 3, 4, 5, 1, 2 ], [ 4, 5, 1, 2, 3 ], [ 5, 1, 2, 3, 4 ] ]
gap>
`
more

I thank you very much for your entire time/answer. That's correct! I will try to identify how to display or produce only positive powers and if I sucess I will post it here. Thank you again!