Rich groups, weak second-order logic, and applications
O Kharlampovich, A Myasnikov… - Groups and Model …, 2021 - degruyter.com
In this chapter we initiate a study of first-order rich groups, ie, groups where the first-order
logic has the same power as the weak second-order logic. Surprisingly, there are quite a few …
logic has the same power as the weak second-order logic. Surprisingly, there are quite a few …
Linear equations with monomial constraints and decision problems in abelian-by-cyclic groups
R Dong - Proceedings of the 2025 Annual ACM-SIAM …, 2025 - SIAM
We show that it is undecidable whether a system of linear equations over the Laurent
polynomial ring ℤ [X±] admit solutions where a specified subset of variables take value in …
polynomial ring ℤ [X±] admit solutions where a specified subset of variables take value in …
Hardness of equations over finite solvable groups under the exponential time hypothesis
A Weiß - arXiv preprint arXiv:2002.10145, 2020 - arxiv.org
Goldmann and Russell (2002) initiated the study of the complexity of the equation
satisfiability problem in finite groups by showing that it is in P for nilpotent groups while it is …
satisfiability problem in finite groups by showing that it is in P for nilpotent groups while it is …
Group equations with abelian predicates
In this paper, we begin the systematic study of group equations with abelian predicates in
the main classes of groups where solving equations is possible. We extend the line of work …
the main classes of groups where solving equations is possible. We extend the line of work …
The Diophantine problem in Chevalley groups
In this paper we study the Diophantine problem in Chevalley groups G π (Φ, R), where Φ is
a reduced irreducible root system of rank> 1, R is an arbitrary commutative ring with 1. We …
a reduced irreducible root system of rank> 1, R is an arbitrary commutative ring with 1. We …
On equations and first-order theory of one-relator monoids
We investigate systems of equations and the first-order theory of one-relator monoids. We
describe a family F of one-relator monoids of the form< A| w= 1> where for each monoid M in …
describe a family F of one-relator monoids of the form< A| w= 1> where for each monoid M in …
The Diophantine problem in the classical matrix groups
AG Myasnikov, M Sohrabi - Izvestiya: Mathematics, 2021 - iopscience.iop.org
The Diophantine problem in the classical matrix groups - IOPscience This site uses cookies.
By continuing to use this site you agree to our use of cookies. To find out more, see our …
By continuing to use this site you agree to our use of cookies. To find out more, see our …
Equation satisfiability in solvable groups
The study of the complexity of the equation satisfiability problem in finite groups had been
initiated by Goldmann and Russell in (Inf. Comput. 178 (1), 253–262,) where they showed …
initiated by Goldmann and Russell in (Inf. Comput. 178 (1), 253–262,) where they showed …
On the Diophantine problem in some one-relator groups
CF Nyberg-Brodda - arXiv preprint arXiv:2208.07145, 2022 - arxiv.org
We study the Diophantine problem, ie the decision problem of solving systems of equations,
for some families of one-relator groups, and provide some background for why this problem …
for some families of one-relator groups, and provide some background for why this problem …
Groups elementarily equivalent to the classical matrix groups
AG Myasnikov, M Sohrabi - Also of Interest, 2018 - degruyter.com
Groups elementarily equivalent to the classical matrix groups Page 63 Alexei G. Myasnikov
and Mahmood Sohrabi Groups Elementarily Equivalent to the Classical Matrix Groups To …
and Mahmood Sohrabi Groups Elementarily Equivalent to the Classical Matrix Groups To …