On nilpotent Chernikov $p$-groups with elementary tops

TL;DR

This paper classifies certain nilpotent Chernikov p-groups with elementary tops by translating the problem into studying tuples of skew-symmetric bilinear forms over finite fields, providing a complete classification in specific cases.

Contribution

It introduces a classification method for nilpotent Chernikov p-groups with elementary tops using quivers with relations, especially when p≠2 and the bottom has two quasi-cyclic summands.

Findings

Complete classification for p≠2 with two quasi-cyclic summands in the bottom

Reduction of the group classification problem to tuples of skew-symmetric bilinear forms

Application of quivers with relations technique

Abstract

The description of nilpotent Chernikov $p$-groups with elementary tops is reduced to the study of tuples of skew-symmetric bilinear forms over the residue field $\mathbb{F}_p$. If $p\ne2$ and the bottom of the group only consists of $2$ quasi-cyclic summands, a complete classification is given. We use the technique of quivers with relations.