[GAP Forum] Needed: Isomorphism onto SmallGroup

[Ken W Smith]

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/