Nilpotent Quotient Algorithm

Question

Does anyone recommend me any reference on the 'Nilpotent quotient algorithm' another book other than D. Johnson "Presentation of groups"? I think that Johnson's example is a bit confusing.

Thanks in advance.

Answer 1

Here are some suggestions, in no particular order. Note that in some cases the material covers in detail the “p-quotient algorithm” as opposed to the nilpotent quotient algorithm. I have found that when speaking to people, sometimes when one refers to one they really mean the other.

Handbook of Computational Group Theory Discrete Mathematics and Its Applications. Authors Derek F. Holt, Bettina Eick, Eamonn A. O'Brien. Chapter 9 is “Computing quotients of finitely presented groups”. There is also a section in Chapter 12 on Verifying Nilpotency. On page 364 the authors give a list of references which includes the book of Sims, mentioned below.

For some online lecture notes about the p-quotient algorithm, which are based on the above book, check out: these notes of Heiko Dietrich.

A very comprehensive book you could try is “Computations with finitely presented groups” by Charles Sims. In particular Chapter 11. If what you really want is the nilpotent quotient algorithm and not the p-quotient algorithm, maybe the coverage here is most detailed.

You can also explore an implementation of the algorithm using the “NQ” package in GAP. Perhaps computing some examples by hand and checking the result in GAP might be helpful. The manual to the NQ package may also help explain some of the background.