Add to ORKGAbstract. In this paper, we study equations over nilpotent groups of class 2. We show that there are some overgroups which contains solutions of equations with exponent sum 1 over nilpotent groups of class 2. As known, equations over a field has a solution in an extension field which contains a copy of the given field. But it is not easy to find that a solution of equations over groups. In many cases, even if equations over groups has a solution, the overgroup is not concrete but very abstract. Here we find the concrete overgroups in case of nilpotent groups. 1
AbstractAn equation over a finite group G is an expression of form w1w2…wk=1G, where each wi is a va...
AbstractIn this paper we study Lamé equations Ln,By=0 in so-called algebraic form, having only algeb...
Let K be any quadratic field with O-K its ring of integers. We study the solutions of cubic equation...
An equation in one variable over a base group is an equation in which one side is a monomial in elem...
If G is a none trivial group and t is an element distinct from G then r(t) =g_1 t^l_1 …......g_kt^l_...
In this thesis we study the theory of equations over a free group. We consider basic notions in com...
AbstractAn algebraic set over a groupGis the set of all solutions of some system {f(x1,…,xn)=1∣f∈G∗〈...
We show that, given a word equation over a finitely generated free group, the set of all solutions i...
Let K be a field of characteristic 0 and let n be a natural number. Let Γ be a subgroup of the multi...
AbstractLet G be a group and 〈x〉 be the free group with generator x. Let w(x) be an element of G ∗ 〈...
This paper is the ninth in a sequence on the structure of sets of solutions to systems of equations ...
AbstractWe investigate the structure of groups satisfying apositive law, that is, an identity of the...
AbstractUsing an analogue of the Makanin–Razborov diagrams, we give a description of the solution se...
Using an analogue of Makanin-Razborov diagrams, we give a description of the solution set of syst...
AbstractWe study the number of solutions of the general semigroup equation in one variable, Xα=Xβ, a...
AbstractAn equation over a finite group G is an expression of form w1w2…wk=1G, where each wi is a va...
AbstractIn this paper we study Lamé equations Ln,By=0 in so-called algebraic form, having only algeb...
Let K be any quadratic field with O-K its ring of integers. We study the solutions of cubic equation...
An equation in one variable over a base group is an equation in which one side is a monomial in elem...
If G is a none trivial group and t is an element distinct from G then r(t) =g_1 t^l_1 …......g_kt^l_...
In this thesis we study the theory of equations over a free group. We consider basic notions in com...
AbstractAn algebraic set over a groupGis the set of all solutions of some system {f(x1,…,xn)=1∣f∈G∗〈...
We show that, given a word equation over a finitely generated free group, the set of all solutions i...
Let K be a field of characteristic 0 and let n be a natural number. Let Γ be a subgroup of the multi...
AbstractLet G be a group and 〈x〉 be the free group with generator x. Let w(x) be an element of G ∗ 〈...
This paper is the ninth in a sequence on the structure of sets of solutions to systems of equations ...
AbstractWe investigate the structure of groups satisfying apositive law, that is, an identity of the...
AbstractUsing an analogue of the Makanin–Razborov diagrams, we give a description of the solution se...
Using an analogue of Makanin-Razborov diagrams, we give a description of the solution set of syst...
AbstractWe study the number of solutions of the general semigroup equation in one variable, Xα=Xβ, a...
AbstractAn equation over a finite group G is an expression of form w1w2…wk=1G, where each wi is a va...
AbstractIn this paper we study Lamé equations Ln,By=0 in so-called algebraic form, having only algeb...
Let K be any quadratic field with O-K its ring of integers. We study the solutions of cubic equation...