[GAP Forum] Working with restriction of WreathProduct's Projection

[Hulpke,Alexander]

Dear Jacob Bond, Dear Forum,


> I have constructed F1 wr A5, where F1 is the free group on 1 generator and A5 is embedded in S12, and have the projection map of the wreath product.

Did you use the generic “WreathProduct” constructor? This will create very general group objects, for which not many special methods exist. You might get better behavior if you construct the wreath product yourself as a finitely presented group.

> However, I would like to restrict the projection to a subgroup of the wreath product given by two generators t0, t1.

What is this subgroup? (Does it have finite index?). To apply the homomorphism GAP needs to be able to decompose elements of the subgroup into a words in t0,t1 which could be difficult.

For initial experiments (just to see how objects get created)  it might be easier to replace F1 with a cyclic group of appropriate order and work in this finite image.

Best,

   Alexander Hulpke

-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke at colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke