Decision Problems in Computational Group Theory

Abstract

In this report we discuss a proof following the ideas of Gabor Elek and Endre Szab that Kaplansky's conjecture is satisfied for group algebras over finite groups and arbitrary fields; as well as, add detail to a proof that Gottschalk's conjecture implies Kaplansky's conjecture over fields with positive characteristics. We further present two algorithms: one is a unique algorithm that, if given an infinite amount of time, can in principle iteratively check Kaplansky's conjecture for all finite groups. The other is a unique implementation of a paper by Dykema, Heister and Juschenko that can check infinite groups from the class of Universal Left Invertible Element (ULIE) groups.

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Document Details

Document Type
Technical Report
Publication Date
Jul 06, 2020
Accession Number
AD1136555

Entities

People

  • Aidan J. Sabety-mass

Organizations

  • United States Naval Academy

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Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.