[GAP Forum] Test for Isoclinism in GAP

Alexander Hulpke hulpke at math.colostate.edu
Thu Oct 14 18:40:39 BST 2010

Dear Forum,

On Oct 6, 2010, at 10/6/10 8:57, Reza Orfi wrote:
> Is there any way to check  that
> two groups are Isoclinism.

I am not aware of any predefined function which does this, so the only solution I can think of is  to write a function  based on the definition:

- Run through all isomorphisms between G/Z and H/Z   (should be sufficient to do this up to inner automorphisms)
- For a sufficient set of elements a,b in G form commutators [a,b] (such that they generate G') and prospective images [c,d] with Za=Zc and Zb=Zd. Test whether this map defines an isomorphism
- If so, test the remaining commutators pairs (up to conjugacy)


  Alexander Hulpke

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

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