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- Ershov, Yu. L. 67 (%)
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## ∏ 1 1 -Completeness of the Computable Categoricity Problem for Projective Planes

### Algebra and Logic (2016-09-01) 55: 283-288 , September 01, 2016

Computable presentations for projective planes are studied. We prove that the problem of computable categoricity is ∏
_{1}^{1}
-complete for the following classes of projective planes: Pappian projective planes, Desarguesian projective planes, arbitrary projective planes.

## Termal and polynomial endomorphisms of universal algebras

### Algebra and Logic (2010-03-01) 49: 12-17 , March 01, 2010

We consider semigroups of termal and polynomial endomorphisms of universal algebras.

## Effectively infinite classes of weak constructivizations of models

### Algebra and Logic (1993-11-01) 32: 342-360 , November 01, 1993

## Absence of the interpolation property in the consistent normal modal extensions of the dummett logic

### Algebra and Logic (1982-11-01) 21: 460-463 , November 01, 1982

## Dominions of universal algebras and projective properties

### Algebra and Logic (2008-09-01) 47: 304-313 , September 01, 2008

Let A be a universal algebra and H its subalgebra. The dominion of H in A (in a class {ie304-01}) is the set of all elements a ∈ A such that every pair of homomorphisms f, g: A → ∈ {ie304-02} satisfies the following: if f and g coincide on H, then f(a) = g(a). A dominion is a closure operator on a set of subalgebras of a given algebra. The present account treats of closed subalgebras, i.e., those subalgebras H whose dominions coincide with H. We introduce projective properties of quasivarieties which are similar to the projective Beth properties dealt with in nonclassical logics, and provide a characterization of closed algebras in the language of the new properties. It is also proved that in every quasivariety of torsion-free nilpotent groups of class at most 2, a divisible Abelian subgroup H is closed in each group 〈H, a〉 generated by one element modulo H.

## The local structure of groups of triangular automorphisms of relatively free algebras

### Algebra and Logic (2012-11-01) 51: 425-434 , November 01, 2012

Let *K* be an arbitrary field and *C*_{n} a relatively free algebra of rank n. In particular, as *C*_{n} we may treat a polynomial algebra *P*_{n}, a free associative algebra *A*_{n}, or an absolutely free algebra *F*_{n}. For the algebras *C*_{n} = *P*_{n}, *A*_{n}, *F*_{n}, it is proved that every finitely generated subgroup *G* of a group *TC*_{n} of triangular automorphisms admits a faithful matrix representation over a field *K*; hence it is residually finite by Mal’tsev’s theorem. For any algebra *C*_{n}, the triangular automorphism group *TC*_{n} is locally soluble, while the unitriangular automorphism group *UC*_{n} is locally nilpotent. Consequently, *UC*_{n} is local (linear and residually finite). Also it is stated that the width of the commutator subgroup of a finitely generated subgroup *G* of *UC*_{n} can be arbitrarily large with increasing n or transcendence degree of a field *K* over the prime subfield.

## Conjugate biprimitive finite groups saturated with finite simple subgroupsU 3(2 n )

### Algebra and Logic (1998-09-01) 37: 345-350 , September 01, 1998

A group G is saturated with groups of the set X if every finite subgroup K≤G is embedded in G into a subgroup L isomorphic to some group of X. We study periodic conjugate biprimitive finite groups saturated with groups in the set {U_{3}(2^{n})}. It is proved that every such group is isomorphic to a simple group U_{3}(Q) over a locally finite field Q of characteristic 2.