Coclass Theory for Finite Nilpotent Associative Algebras: Algorithms and a Periodicity Conjecture

We describe two algorithms that allow to investigate the graph G(F) (r) associated with the nilpotent associative F-algebras of coclass r for a finite field F and a non-negative r. Based on experimental evidence obtained via these algorithms, we conjecture that G(F) (r) is virtually periodic for each finite field F and each r. If this periodicity conjecture holds, then it suggests that for each finite field F and each r the infinitely many nilpotent associative F-algebras of coclass r can be classified by a finite set of data.