Balanced finite presentations of the trivial group
Boris Lishak

TL;DR
This paper constructs a sequence of balanced finite presentations of the trivial group where the minimal number of relations needed to prove triviality grows faster than any fixed-height exponential tower relative to the presentation length.
Contribution
It introduces a novel sequence of balanced presentations demonstrating extremely complex triviality proofs, surpassing previous complexity bounds.
Findings
Minimal relations grow faster than any fixed-height exponential tower
Demonstrates extreme complexity in trivial group presentations
Provides new insights into the complexity of group triviality proofs
Abstract
We construct a sequence of balanced finite presentations of the trivial group with two generators and two relators with the following property: The minimal number of relations required to demonstrate that a generator represents the trivial element grows faster than the tower of exponentials of any fixed height of the length of the finite presentation.
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