Pseudocharacters on free products of semigroups

Pseudocharacters on free semigroups invariant with respect to their automorphism groups

“…See Lemma 13 in [17]. Theorem 1] we obtain that the functions δ w and δ w are pseudocharacters of the semigroup F .…”

“…In [12]- [17] a description of the spaces of pseudocharacters on free groups and semigroups, semidirect and free products of semigroups was given.…”

“…For any element w of F such that H(w) ∩ K(w) = ∅ in [17] the functions η w and e w were defined as follows: if v ∈ F, then η w (v) is equal to the number of occurrences of w in the word v; e w = max{η w (v ), v ∼ v} .…”

Pseudocharacters and the Problem of Expressibility for Some Groups

“…We say that a pseudocharacter ϕ of the group G is nontrivial if ϕ ∈ X G . In the papers [5][6][7][10][11][12], a description of the set of pseudocharacters of free groups and semigroups, on the free and semidirect products of groups and semigroups, was given.…”

The space of (𝜓,𝛾)–additive mappings on semigroups

“…In [5] the set of all pseudocharacters of free groups was described. In [4]- [9] a description of the spaces of pseudocharacters on free groups, semigroups, free products of semigroups, and on some extensions of free groups was given. For a mapping f of the group G into the semigroup of linear transformations of a vector space, sufficient conditions for the coincidence of the solution of the functional inequality f (xy)−f (x)·f (y) < c with the solution of the corresponding functional equation f (xy) − f (x) · f (y) = 0 were studied in [2,14,24].…”