Abstract: We give a criterion for the countable spectrum to be maximal in small binary quite o-minimal theories of finite convexity rank. PubDate: 2019-07-20

Abstract: Let σ = {σi i ∈ I} be a partition of the set of all primes ℙ and G a finite group. Suppose σ(G) = {σi σi ∩ π(G) ≠ = ∅}. A set ℋ of subgroups of G is called a complete Hall σ-set of G if every nontrivial member of ℋ is a σi-subgroup of G for some i ∈ I and ℋ contains exactly one Hall σi-subgroup of G for every i such that σi ∈ σ(G). A group G is σ-full if G possesses a complete Hall σ-set. A complete Hall σ-set ℋ of G is called a σ-basis of G if every two subgroups A, B ∈ ℋ are permutable, i.e., AB = BA. In this paper, we study properties of finite groups having a σ-basis. It is proved that if G has a σ-basis, then G is generalized σ-soluble, i.e, σ(H/K) ≤ 2 for every chief factor H/K of G. Moreover, it is shown that every complete Hall σ-set of a σ-full group G forms a σ-basis of G iff G is generalized σ-soluble, and for the automorphism group G/CG(H/K) induced by G on any its chief factor H/K, we have σ(G/CG(H/K)) ≤ 2 and also σ(H/K) ⊆ σ(G/CG(H/K)) in the case σ(G/CG(H/K)) = 2. PubDate: 2019-07-20

Abstract: The concept of a generalized wreath product of permutation m-groups is introduced, and it is proved that an m-transitive permutation group embeds into a generalized wreath product of its primitive components. PubDate: 2019-07-20

Abstract: The interpolation problem over Johansson’s minimal logic J is considered. We introduce a series of Johansson algebras, which will be used to prove a number of necessary conditions for a J-logic to possess Craig’s interpolation property (CIP). As a consequence, we deduce that there exist only finitely many finite-layered pre-Heyting algebras with CIP. PubDate: 2019-07-20

Abstract: Functions of the algebra of logic that can be realized by read-once formulas over finite bases are studied. Necessary and sufficient conditions are derived under which functions of the algebra of logic are read-once in pre-elementary bases {−, ·,∨, 0, 1, x1 · . . . · xn ∨ \( {\overline{x}}_1 \) · . . . · \( {\overline{x}}_n \) } and {−, ·,∨, 0, 1, x1(x2 ∨ x3 · . . . · xn) ∨ x2 \( {x}_2{\overline{x}}_3 \) · . . . · \( {\overline{x}}_n \) } where n ≥ 4. This completes the description of classes of read-once functions of the algebra of logic in all pre-elementary bases. PubDate: 2019-07-20

Abstract: It is proved that the property of being a semisimple algebra is preserved under projections (lattice isomorphisms) for locally finite-dimensional Lie algebras over a perfect field of characteristic not equal to 2 and 3, except for the projection of a three-dimensional simple nonsplit algebra. Over fields with the same restrictions, we give a lattice characterization of a three-dimensional simple split Lie algebra and a direct product of a one-dimensional algebra and a three-dimensional simple nonsplit one. PubDate: 2019-07-20

Abstract: Sufficient conditions are specified under which a quasivariety contains continuum many subquasivarieties having an independent quasi-equational basis but for which the quasiequational theory and the finite membership problem are undecidable. A number of applications are presented. PubDate: 2019-07-20

Abstract: A standard way to capture the inherent complexity of the isomorphism type of a countable structure is to consider the set of all Turing degrees relative to which the given structure has a computable isomorphic copy. This set is called the degree spectrum of a structure. Similarly, to characterize the complexity of models of a theory, one may examine the set of all degrees relative to which the theory has a computable model. Such a set of degrees is called the degree spectrum of a theory. We generalize these two notions to arbitrary equivalence relations. For a structure \( \mathcal{A} \) and an equivalence relation E, the degree spectrum DgSp( \( \mathcal{A} \) , E) of \( \mathcal{A} \) relative to E is defined to be the set of all degrees capable of computing a structure \( \mathcal{B} \) that is E-equivalent to \( \mathcal{A} \) . Then the standard degree spectrum of \( \mathcal{A} \) is DgSp( \( \mathcal{A} \) , ≅) and the degree spectrum of the theory of \( \mathcal{A} \) is DgSp( \( \mathcal{A} \) , ≡). We consider the relations \( {\equiv}_{\sum_n} \) ( \( \mathcal{A}{\equiv}_{\sum_n}\mathcal{B} \) iff the Σn theories of \( \mathcal{A} \) and \( \mathcal{B} \) coincide) and study degree spectra with respect to \( {\equiv}_{\sum_n} \) . PubDate: 2019-07-20

Abstract: Universal enveloping Lie Rota–Baxter algebras of pre-Lie and post-Lie algebras are constructed. It is proved that the pairs of varieties (RBLie, preLie) and (RBλLie, postLie) are PBW-pairs and that the variety of Lie Rota–Baxter algebras is not a Schreier variety. PubDate: 2019-05-30

Abstract: It is stated that the second Hochshild cohomology group of the associative conformal algebra Cend1,x with values in any bimodule is trivial. Consequently, the given algebra splits off in every extension with nilpotent kernel. PubDate: 2019-05-30

Abstract: We classify simple right-alternative unital superalgebras over a field of characteristic not 2, whose even part coincides with an algebra of matrices of order 2. It is proved that such a superalgebra either is a Wall double W2 2(ω), or is a Shestakov superalgebra S4 2(σ) (characteristic 3), or is isomorphic to an asymmetric double, an 8-dimensional superalgebra depending on four parameters. In the case of an algebraically closed base field, every such superalgebra is isomorphic to an associative Wall double M2[√1], an alternative 6-dimensional Shestakov superalgebra B4 2 (characteristic 3), or an 8-dimensional Silva–Murakami–Shestakov superalgebra. PubDate: 2019-05-30

Abstract: We study the structure of an infinite group with automorphism of order 2p, where p is an odd prime leaving only the identity element fixed. PubDate: 2019-05-30

Abstract: Associative rings R and R′ are said to be lattice-isomorphic if their subring lattices L(R) and L(R′) are isomorphic. An isomorphism of the lattice L(R) onto the lattice L(R′) is called a projection (or lattice isomorphism) of the ring R onto the ring R′. A ring R′ is called the projective image of a ring R. Whenever a lattice isomorphism φ implies an isomorphism between R and Rφ, we say that the ring R is determined by its subring lattice. The present paper is a continuation of previous research on lattice isomorphisms of finite rings. We give a complete description of projective images of prime and semiprime finite rings. One of the basic results is the theorem on lattice definability of a matrix ring over an arbitrary Galois ring. Projective images of finite rings decomposable into direct sums of matrix rings over Galois rings of different types are described. PubDate: 2019-05-30

Abstract: Numerical characteristics of polynomial identities of left nilpotent algebras are examined. Previously, we came up with a construction which, given an infinite binary word, allowed us to build a two-step left nilpotent algebra with specified properties of the codimension sequence. However, the class of the infinite words used was confined to periodic words and Sturm words. Here the previously proposed approach is generalized to a considerably more general case. It is proved that for any algebra constructed given a binary word with subexponential function of combinatorial complexity, there exists a PI-exponent. And its precise value is computed. PubDate: 2019-05-30

Abstract: For finite simple groups U5(2n), n > 1, U4(q), and S4(q), where q is a power of a prime p > 2, q − 1 ≠= 0(mod4), and q ≠= 3, we explicitly specify generating triples of involutions two of which commute. As a corollary, it is inferred that for the given simple groups, the minimum number of generating conjugate involutions, whose product equals 1, is equal to 5. PubDate: 2019-05-30

Abstract: We find a sufficient condition for a quasivariety K to have continuum many subquasivarieties that have no independent quasi-equational bases relative to K but have ω-independent quasi-equational bases relative to K. This condition also implies that K is Q-universal. PubDate: 2019-03-22