Dear Siddhartha,
On 31 Mar 2009, at 12:02, Siddhartha Sarkar wrote:
Dear GAP forum,
I am trying to access the group of order 2^8 which has the
descripton :
(1) it is of co-class 2,
(2) cited as G_20 and from family 8 (in the paper by Baginski,
Konovalov
"On 2-groups of Almost Maximal Class"); maybe these notations are
standard.
No, we used the numeration for families following the paper by M. F.
Newman and
E. A. O’Brien, Classifying 2-groups by coclass. Trans. A.M.S., vol.
351, No.1,
January 1999, 131-169, but the numbering of groups is only used within
our paper.
How to find this in the small group library?
The presentation is :
Generators : x_1, x_2, y
Relations : x_1^8 = x_2^8 = 1, y^4 = x_2^4, x_1^y = x_1 * x_2, x_2^y =
x_1^{-2} * x_2^3, [x_2, x_1] = 1
This is the group [ 256, 519 ]:
gap> f:=FreeGroup("x_1","x_2","y");
<free group on the generators [ x_1, x_2, y ]>
gap> AssignGeneratorVariables(f);
#I Assigned the global variables [ x_1, x_2, y ]
gap> r:=[x_1^8,x_2^8,y^4*x_2^4,y^-1*x_1*y*x_2^-1*x_1^-1,
> y^-1*x_2*y*x_2^-3*x_1^2,x_1^-1*x_2^-1*x_1*x_2];
[ x_1^8, x_2^8, y^4*x_2^4, y^-1*x_1*y*x_2^-1*x_1^-1,
y^-1*x_2*y*x_2^-3*x_1^2,
x_1^-1*x_2^-1*x_1*x_2 ]
gap> G:=f/r;
<fp group on the generators [ x_1, x_2, y ]>
gap> IdGroup(G);
[ 256, 519 ]
Please let me know if you will have further questions.
Best wishes,
Alexander
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