New Andrews–Curtis trivializations for Miller–Schupp group presentations

• Published in: Examples and counterexamples Vol. 6; p. 100168
• Main Author: Lisitsa, Alexei
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2024; Elsevier
• Subjects: AC-trivializations; Andrews–Curtis conjecture; Automated theorem proving; Combinatorial group theory; Combinatorial group theory; AC-trivializations; Automated theorem proving; Andrews–Curtis conjecture
• ISSN: 2666-657X; 2666-657X
• DOI: 10.1016/j.exco.2024.100168

We present recent developments in the applications of automated theorem proving in the investigation of the Andrews–Curtis conjecture. We demonstrate previously unknown trivializations of group presentations from a parametric family MSn(w∗) of trivial group presentations for n=3,4,5,6,7,8 (subset of well-known Miller–Schupp family). Based on the human analysis of these trivializations we formulate two conjectures on the structure of simplifications for the infinite family MSn(w∗), n≥3. •New examples of Andrews–Curtis trivilaizations are demonstrated.•Two conjectures on structural properties of trivializations sequences are presented.•The strength of generic automated reasoning methods in group theory is demonstrated.