Towards parametrizing word equations

H. Abdulrab; P. Goralčík; G. S. Makanin

Displaying similar documents to “Towards parametrizing word equations”

Three-variable equations of posets

Jaroslav Ježek (2002)

Czechoslovak Mathematical Journal

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We find an independent base for three-variable equations of posets.

Constructions of (2,n)-varieties of groupoids for n = 7, 8, 9

Lidija Goraèinova-Ilieva, Smile Markovski (2007)

Publications de l'Institut Mathématique

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Solution of Whitehead equation on groups

Valeriĭ A. Faĭziev, Prasanna K. Sahoo (2013)

Mathematica Bohemica

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Let $G$ be a group and $H$ an abelian group. Let $J^{*} (G, H)$ be the set of solutions $f : G \to H$ of the Jensen functional equation $f (x y) + f (x y^{- 1}) = 2 f (x)$ satisfying the condition $f (x y z) - f (x z y) = f (y z) - f (z y)$ for all $x, y, z \in G$ . Let $Q^{*} (G, H)$ be the set of solutions $f : G \to H$ of the quadratic equation $f (x y) + f (x y^{- 1}) = 2 f (x) + 2 f (y)$ satisfying the Kannappan condition $f (x y z) = f (x z y)$ for all $x, y, z \in G$ . In this paper we determine solutions of the Whitehead equation on groups. We show that every solution $f : G \to H$ of the Whitehead equation is of the form $4 f = 2 ϕ + 2 ψ$ , where $2 ϕ \in J^{*} (G, H)$ and $2 ψ \in Q^{*} (G, H)$ . Moreover, if $H$ has the additional property that $2 h = 0$ implies $h = 0$ for all $h \in H$ ,...

A note on finite sets of terms closed under subterms and unification

Jaroslav Ježek (1996)

Commentationes Mathematicae Universitatis Carolinae

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The paper contains two remarks on finite sets of groupoid terms closed under subterms and the application of unifying pairs.

The free commutative automorphic $2$ -generated loop of nilpotency class $3$

Dylene Agda Souza de Barros, Alexander Grishkov, Petr Vojtěchovský (2012)

Commentationes Mathematicae Universitatis Carolinae

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A loop is automorphic if all its inner mappings are automorphisms. We construct the free commutative automorphic $2$ -generated loop of nilpotency class $3$ . It has dimension $8$ over the integers.

Displaying similar documents to “Towards parametrizing word equations”

Three-variable equations of posets

Constructions of (2,n)-varieties of groupoids for n = 7, 8, 9

Solution of Whitehead equation on groups

A note on finite sets of terms closed under subterms and unification

The free commutative automorphic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mn>2</mn> </math>-generated loop of nilpotency class <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mn>3</mn> </math>

The free commutative automorphic $2$ -generated loop of nilpotency class $3$