## Today is a good day

Step by step. This could the adage of my work. Slowly. Patiently.

Today is a great day. I work hard since several months (neally a year) on the isomorphism problem in groups (google it, if you don’t know what is it).

Having worked neally all the week end on an idea that surged last week, I can say that for the first time, If you give me 2 Cayley Tables of finite groups, I can say if these Cayley Tables are isomorphic or not by computing special normalized presentations. It probably does not work in all cases but it works for a lot of them.

I know some cases for which what I have done, does not work, but I know how to improve quite easily these cases. There are probably some couples of Cayley Tables for which I can’t say if they are isomorphic or not, but for the moment I don’t see them.

Actually I feel good, very good. It won’t last (as usual) because I will pretty soon find another wall but for the moment I’m just peaceful.

I should definitely study in detail power commutator presentations (I think Sylow was their discoverer) which are used by Eamon O’Brien to compute the groups of orders 256 and 512 and PolyCyclic Generating Sequences which are used by Bettina Eick to compute automorphisms of p-groups. Knowing these specific presentations, I could compare them with my own presentation and study their respective properties.