10 citations · 28 across the 6 of their papers we have counts for
7 papers
Finitely generated subgroups of free groups as formal languages and their cogrowth
Arman Darbinyan, Rostislav Grigorchuk, Asif Shaikh
For finitely generated subgroups of a free group of finite rank , we study the language of reduced words that represent which is a regular language. Using th…
Embeddings into left-orderable simple groups
Arman Darbinyan, Markus Steenbock
We prove that every countable left-ordered group embeds into a finitely generated left-ordered simple group. Moreover, if the first group has a computable left-order, then the simp…
Computability, orders, and solvable groups
Arman Darbinyan
The main objective of this paper is the following two results. (1) There exists a computable bi-orderable group that does not have a computable bi-ordering; (2) There exists a bi-o…
Group Embeddings with Algorithmic Properties
Arman Darbinyan
We show that every countable group H with solvable word problem (=computable group) can be subnormally embedded into a 2-generated group G which also has solvable word problem. Mor…
Groups with decidable word problem that do not embed in groups with decidable conjugacy problem
Arman Darbinyan
We show the existence of finitely presented torsion-free groups with decidable word problem that cannot be embedded in any finitely generated group with decidable conjugacy problem…
The word and conjugacy problems in lacunary hyperbolic groups
Arman Darbinyan
We study the word and conjugacy problems in lacunary hyperbolic groups (briefly, LHG). In particular, we describe a necessary and sufficient condition for decidability of the word…