An inductive method for separable deformations

TL;DR

This paper introduces an inductive approach to deform group algebras, successfully proving the Donald-Flanigan conjecture for an infinite family of metacyclic groups by building from normal subgroup deformations.

Contribution

It presents a novel inductive method for deforming group algebras, extending the class of groups known to satisfy the Donald-Flanigan conjecture.

Findings

Established the conjecture for an infinite family of metacyclic groups

Developed an inductive framework for algebra deformations

Connected subgroup deformations to group algebra properties

Abstract

The Donald-Flanigan conjecture asserts that any group algebra of a finite group has a separable deformation. We apply an inductive method to deform group algebras from deformations of normal subgroup algebras, establishing an infinite family of metacyclic groups which fulfill the conjecture.