MIDN 1/C Aidan J. Sabety-Mass - 25th Company

Decision Problems in Computational Group Theory

Adviser: Associate Professor Kostya Medynets, Mathematics Department
Major: Mathematics (Honors)

Description: 
This Trident research project has completed and implemented a Python script to check Kaplansky’s Direct Finiteness Conjecture for finite groups. We have also implemented a program to check Kaplansky’s Conjecture for infinite groups with finite generators, called Universal Left Invertible Elements (ULIE). We have proved and worked on the theoretical aspects of decision problems, solving word problems and creating confluent rewriting systems. Additionally, we have produced an alternate proof for confirming that Kaplansky’s Conjecture is satisfied for finite groups. We have also successfully parallelized our Python program for multiprocessing on multiple CPUs. Along with this, we have finished the implementation of another parallelized program checking ULIE groups in SAGE.

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