[GAP Forum] Reduced Multiplication

Sopsku rrburns at cox.net
Mon Aug 26 03:54:23 BST 2013


Hi all,
I have some small confusion about reduced multiplication that I would like
to clear up. Suppose I have:

gap> d4:=DihedralGroup(IsFpGroup,4);;
gap> r:=d4.1;;s:=d4.2;;
gap> SetReducedMultiplication(d4);

Then 

gap> r^2;
<identity ...>

OK - now suppose I look at 

gap> rel:=RelatorsOfFpGroup(d4);
[ r^2, s^2, s^-1*r*s*r ]

rel does not reduce and I guess that makes sense as I would want to see the
the relations not <identitly ...>. Now if I cut and paste

gap> [ r^2, s^2, s^-1*r*s*r ];
[ <identity ...>, <identity ...>, <identity ...> ]

Is there an function that I can apply to rel to force the reduced
multiplication without the cut and paste? 

I tried copies and tests like

gap> rel[1]=Identity(d4);
false

but even  this does not do the reduction before the test.

Thanks for any comments
     Ron






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