Compressed primitivity problem in free groups
Year: 2026
Type: article
Abstract: For a fixed integer r ≥ 2 , we prove that the compressed primitivity problem in the free group F r = F ( x 1 , … , x r ) is decidable in nondeterministic polynomial time. That is, for a straight-line program A over { x 1 , … , x r } ± 1 representing an element g ∈ F r , the problem of deciding whether g is primitive in F r belongs to NP , with input measured by the size of A . For r = 2 , we prove that this problem is decidable in deterministic polynomial time. We also show that, in every fixed rank r ≥ 2 , automorphic minimality of the conjugacy class of a compressed word in F r is decidable in deterministic polynomial time.
Source: Journal of Computational Algebra
Author: Ilya Kapovich
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,860
OpenAlex ID: W7170789052