Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New results on the prefix membership problem for one-relator groups   In this paper we prove several results regarding decidability of the
membership problem for certain submonoids in amalgamated free products and HNN
extensions of groups. These general results are then applied to solve the
prefix membership problem for a number of classes of one-relator groups which
are low in the Magnus-Moldavanski\u{\i} hierarchy. Since the prefix membership
problem for one-relator groups is intimately related to the word problem for
one-relator special inverse monoids in the $E$-unitary case (as discovered in
2001 by Ivanov, Margolis and Meakin), these results yield solutions of the word
problem for several new classes of one-relator special inverse monoids. In
establishing these results, we introduce a new theory of conservative
factorisations of words which provides a link between the prefix membership
problem of a one-relator group and the group of units of the corresponding
one-relator special inverse monoid. Finally, we exhibit the first example of a
one-relator group, defined by a reduced relator word, that has an undecidable
prefix membership problem.

12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th