Hi,
I am constructing a database of certain combinatorial subsets of
finite groups and I would like to use GAP's Small Group library to
provide a standard way of referencing the groups in my list and certain
subsets of these groups. But in order to do this, I need code that
constructs an explicit isomorphism between a finite group (with a given
presentation) and an isomorphic group in the Small Groups library.
I have hundreds of examples like the following. Suppose we have a
group, say,
G := < x, y, z : x^5 = y^5 = z^4 = [x,y] = z*x*z^-1*x^3 =
z*y*z^-1*y^3 >
and a special subset of G, say,
D = {1, x, x^2, x*y, x*y*z^2, x^-1*y^2*z^3}.
GAP tells me that G is isomorphic to the group [100,11] in the Small
Group Library. But now I need an explicit isomorphism from G onto
SmallGroup( 100, 11 ) so that I can identify the set D with some subset
of Elements( SmallGroup( 100, 11 ) ). Is there a convenient way to
do this? (Note that the SmallGroup library views groups of order 100
as having 4 generators ... and I've given a different presentation,
using 3 generators.)
Any help here will be greatly appreciated!
thanks,
Ken
---
Ken W. Smith, Professor of Mathematics, Central Michigan University
989-774-6521 (W), 774-2414 (Fax), 854-0185 (Cell)
http://calcnet.cst.cmich.edu/faculty/smith/
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