On Irreducible Cyclic Presentations of the Trivial Group

Abstract

This article details a series of computational group theory experiments involving a search for irreducible cyclic presentations of the trivial group. The list of such presentations obtained provides test cases for the Andrews–Curtis conjecture.

2000 AMS Subject Classification::

• Primary 20F05
• Secondary 57M20

• group
• cyclic presentation

Notes

¹The interested reader can view the remaining 67 that occur when n < 4 at https://www.maths.nottingham.ac.uk/personal/me/ , where there are listed all w for which G_n(w) is trivial and all the w(x, t) for which the triviality of the corresponding G_n(w) is undecided when l ≤ 17 and 2 ≤ n ≤ 100.