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.

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 → 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 ∈ G . Let Q * ( G , H ) be the set of solutions f : G → 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 ∈ G . In this paper we determine solutions of the Whitehead equation on groups. We show that every solution f : G → H of the Whitehead equation is of the form 4 f = 2 ϕ + 2 ψ , where 2 ϕ ∈ J * ( G , H ) and 2 ψ ∈ Q * ( G , H ) . Moreover, if H has the additional property that 2 h = 0 implies h = 0 for all h ∈ H ,...