New Andrews–Curtis trivializations for Miller–Schupp group presentations
Year: 2024
Type: article
Abstract: 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 M S n ( 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 M S n ( 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.
Source: Examples and Counterexamples
Author: Alexei Lisitsa
Institution: University of Liverpool
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $330
OpenAlex ID: W4404116779