In this paper we study the complexity of solving quadratic equations in the lamplighter group.
We give a complete classification of cases (depending on genus and other characteristics of …

Orientable quadratic equations in free metabelian groups - ScienceDirect Skip to main
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If u and v are two conjugate elements of a hyperbolic group then the length of a shortest
conjugating element for u and v can be bounded by a linear function of the sum of their …

In this paper we analyze computational properties of the Diophantine problem (and its
search variant) for spherical equations∏ mi= 1 z− 1 i cizi= 1 (and their variants) over the …

In this paper we investigate computational properties of the Diophantine problem for
spherical equations in some classes of finite groups G. We classify the complexity of different …

Consider the equation q 1 α x 1+…+ qk α xk= q, with constants α∈ Q‾∖{0, 1}, q 1,…, qk, q∈
Q‾ and unknowns x 1,…, xk, referred to in this paper as an algebraic equation with …

The problem of assignment and sequencing of tasks is a very complex problem, which is
related to whether the computer system can effectively exert the overall efficiency. Solving …

The paper is a part of an ongoing program which aims to show that the problem of
satisfiability of a system of equations in a free group (hyperbolic or even toral relatively …

We investigate systems of equations and the first-order theory of one-relator monoids and of
word-hyperbolic monoids. We describe a family of one-relator monoids of the form⟨ A∣ w …

For g≥ 1 denote by F 2 g=〈 x 1, y 1,…, xg, yg〉 the free group on 2 g generators and let B
g=[x 1, y 1]⋯[xg, yg]. For l, c≥ 1 and elements w 1,…, wl∈ F 2 g, we study orientable …