Lifting property for finite groups

TL;DR

This paper classifies all finite groups that allow lifting of mod p representations to mod p^2 representations across all primes p, providing a comprehensive understanding of this lifting property.

Contribution

It offers a complete classification of finite groups with the lifting property for mod p representations to mod p^2 for all primes p.

Findings

Identifies all finite groups with the lifting property.

Provides criteria for the lifting property across all primes.

Advances understanding of representation lifting in finite groups.

Abstract

We classify all finite groups that have lifting property of mod $p$ representations to mod $p^2$ representations for all prime $p$.