What question did this study set out to answer?

The aim is to classify maximal nilpotent linear subspaces for fields with at least two elements, extending prior research on fields with more members.

June 14, 2026

Nilpotent linear spaces in M 4 (ℤ2)

Key Points

The aim is to classify maximal nilpotent linear subspaces for fields with at least two elements, extending prior research on fields with more members.
Combined algebraic arguments with computational verification methods over finite fields
Focused on nilpotent linear subspaces in the context of M4 over Z2
Completed the classification of maximal nilpotent linear subspaces for arbitrary finite fields
Established relationships among nilpotent linear spaces up to similarity for the case of finite fields

Abstract

In 4, the maximal nilpotent linear subspaces of Formula: see text were classified, up to similarity, for fields Formula: see text with at least three elements. In the present paper, we extend this classification to the case Formula: see text. Our approach combines algebraic arguments with systematic computational verification over the finite field Formula: see text. This completes the classification of maximal nilpotent linear subspaces of Formula: see text for arbitrary fields Formula: see text.

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