On Projective Representations of Special p-groups

TL;DR

This paper characterizes the complex irreducible projective representations of special p-groups under specific rank conditions, expanding understanding of their representation theory.

Contribution

It provides a detailed description of projective representations for special p-groups of rank two or maximum rank with certain size constraints.

Findings

Descriptions of irreducible projective representations for rank two groups.

Characterization of representations for maximum rank groups with limited $|G^p|$.

Enhanced understanding of the structure of special p-groups' representations.

Abstract

Let $G$ be a special $p$-group. If $G$ is of rank two, or $G$ is of maximum rank with $|G^p|\leq p$, then we describe the complex irreducible projective representations of $G$.