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

ABSTRACT

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

KEYWORDS:

• coclass theory
• nilpotent associative algebras
• p-groups

2000 AMS SUBJECT CLASSIFICATION:

• 16N40
• 16W99
• 16Z05
• 20D15