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Publisher: Springer-Verlag   (Total: 2335 journals)

 Algebra and Logic   [SJR: 0.566]   [H-I: 18]   [2 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 1573-8302 - ISSN (Online) 0002-5232    Published by Springer-Verlag  [2335 journals]
• Structures Computable in Polynomial Time. I
• Authors: P. E. Alaev
Pages: 421 - 435
Abstract: It is proved that every computable locally finite structure with finitely many functions has a presentation computable in polynomial time. Furthermore, a structure computable in polynomial time is polynomially categorical iff it is finite. If a structure is computable in polynomial time and locally finite then it is weakly polynomially categorical (i.e., categorical with respect to primitive recursive isomorphisms) iff it is finite.
PubDate: 2017-01-01
DOI: 10.1007/s10469-017-9416-y
Issue No: Vol. 55, No. 6 (2017)

• Subgroups, Automorphisms, and Lie Algebras Related to the
Basis-Conjugating Automorphism Group
• Authors: V. G. Bardakov; M. V. Neshchadim
Pages: 436 - 460
Abstract: We study some subgroups of the automorphism group of a free group, their factorizations into a semidirect product, automorphism groups, and adjoint Lie algebras.
PubDate: 2017-01-01
DOI: 10.1007/s10469-017-9417-x
Issue No: Vol. 55, No. 6 (2017)

• Freely Generated Projective Planes with Finite Computable Dimension
• Authors: N. T. Kogabaev
Pages: 461 - 484
Abstract: It is proved that for every natural n ≥ 1, there exists a computable freely generated projective plane with computable dimension n. It is stated that the class of freely generated projective planes is complete with respect to degree spectra of automorphically nontrivial structures, effective dimensions, expansions by constants, and degree spectra of relations.
PubDate: 2017-01-01
DOI: 10.1007/s10469-017-9418-9
Issue No: Vol. 55, No. 6 (2017)

• Spectrum of the Field of Computable Real Numbers
• Authors: M. V. Korovina; O. V. Kudinov
Pages: 485 - 500
Abstract: Necessary and sufficient conditions for a Turing degree to be an element of the spectrum of the classical field of computable real numbers are established.
PubDate: 2017-01-01
DOI: 10.1007/s10469-017-9419-8
Issue No: Vol. 55, No. 6 (2017)

• Algebraically Equivalent Clones
• Authors: A. G. Pinus
Pages: 501 - 506
Abstract: Two functional clones F and G on a set A are said to be algebraically equivalent if sets of solutions for F- and G-equations coincide on A. It is proved that pairwise algebraically nonequivalent existentially additive clones on finite sets A are finite in number. We come up with results on the structure of algebraic equivalence classes, including an equationally additive clone, in the lattices of all clones on finite sets.
PubDate: 2017-01-01
DOI: 10.1007/s10469-017-9420-2
Issue No: Vol. 55, No. 6 (2017)

• Generalized Hyperarithmetical Computability Over Structures
• Authors: A. I. Stukachev
Pages: 507 - 526
Abstract: We consider the class of approximation spaces generated by admissible sets, in particular by hereditarily finite superstructures over structures. Generalized computability on approximation spaces is conceived of as effective definability in dynamic logic. By analogy with the notion of a structure Σ-definable in an admissible set, we introduce the notion of a structure effectively definable on an approximation space. In much the same way as the Σ-reducibility relation, we can naturally define a reducibility relation on structures generating appropriate semilattices of degrees of structures (of arbitrary cardinality), as well as a jump operation. It is stated that there is a natural embedding of the semilattice of hyperdegrees of sets of natural numbers in the semilattices mentioned, which preserves the hyperjump operation. A syntactic description of structures having hyperdegree is given.
PubDate: 2017-01-01
DOI: 10.1007/s10469-017-9421-1
Issue No: Vol. 55, No. 6 (2017)

• Sessions of the Seminar “Algebra i Logika”
• Pages: 527 - 527
PubDate: 2017-01-01
DOI: 10.1007/s10469-017-9422-0
Issue No: Vol. 55, No. 6 (2017)

• Abnormality Criteria for p -Complements
• Authors: E. P. Vdovin; D. O. Revin
Pages: 347 - 353
Abstract: It is proved that for any finite group G possessing a p-complement H for some prime number p, the following assertions are equivalent: (1) all p-complements of G are self-normalizable; (2) all p-complements of G are abnormal; (3) the subgroup H is abnormal in G; (4) NG(HX) = HX for any \( X\underline{\vartriangleleft}\;G \) ; (5) G does not contain central chief p-factors.
PubDate: 2016-11-01
DOI: 10.1007/s10469-016-9406-5
Issue No: Vol. 55, No. 5 (2016)

• Spectra of Automorphic Extensions of Finite Simple Exceptional Groups of
Lie Type
• Authors: M. A. Zvezdina
Pages: 354 - 366
Abstract: The spectrum ω (G) of a finite group G is the set of orders of elements of G. Let S be a simple exceptional group of type E 6 or E 7 . We describe all finite groups G such that S ≤ G ≤ Aut S and ω (G) = ω (S) and completes the study of the recognition-by-spectrum problem for all simple exceptional groups of Lie type.
PubDate: 2016-11-01
DOI: 10.1007/s10469-016-9407-4
Issue No: Vol. 55, No. 5 (2016)

• Permutation Groups in Categorical Additive Horn Theories
• Authors: E. A. Palyutin
Pages: 407 - 411
PubDate: 2016-11-01
DOI: 10.1007/s10469-016-9413-6
Issue No: Vol. 55, No. 5 (2016)

• Sessions of the Seminar “Algebra i Logika”
• Pages: 419 - 420
PubDate: 2016-11-01
DOI: 10.1007/s10469-016-9415-4
Issue No: Vol. 55, No. 5 (2016)

• Algebraic Geometry Over Completely Simple Semigroups
• Authors: P. A. Ulyashev
Abstract: Algebraic geometry over completely simple semigroups is considered. We prove theorems that define coordinate semigroups and irreducible coordinate semigroups in several classes of completely simple semigroups.
PubDate: 2016-12-01
DOI: 10.1007/s10469-016-9411-8

• Supergeneric Equations
• Authors: B. Poizat
PubDate: 2016-12-01
DOI: 10.1007/s10469-016-9414-5

• The Centralizer Dimension of Generalized Baumslag–Solitar Groups
• Authors: F. A. Dudkin
PubDate: 2016-12-01
DOI: 10.1007/s10469-016-9412-7

• Levi Decomposition for Carpet Subgroups of Chevalley Groups Over a Field
• Authors: Ya. N. Nuzhin
Abstract: It is proved that a carpet subgroup of a Chevalley group of type Φ over a field is a semidirect product whose kernel is defined by a unipotent carpet of type Φ, while the noninvariant factor is a central product of carpet subgroups each of which is defined by an irreducible subcarpet of type Φi for some indecomposable root subsystem Φ i of Φ. The obtained result can be viewed as an analog of the Levi decomposition.
PubDate: 2016-12-01
DOI: 10.1007/s10469-016-9408-3

• Partially Divisible Completions of Rigid Metabelian Pro- p -groups
• Authors: N. S. Romanovskii
Abstract: Previously, the author defined the concept of a rigid (abstract) group. By analogy, a metabelian pro-p-group G is said to be rigid if it contains a normal series of the form G = G1 ≥ G2 ≥ G3 = 1 such that the factor group A = G/G2 is torsion-free Abelian, and G2 being a ZpA-module is torsion-free. An abstract rigid group can be completed and made divisible. Here we do something similar for finitely generated rigid metabelian pro-p-groups. In so doing, we need to exit the class of pro-p-groups, since even the completion of a torsion-free nontrivial Abelian pro-p-group is not a pro-p-group. In order to not complicate the situation, we do not complete a first factor, i.e., the group A. Indeed, A is simply structured: it is isomorphic to a direct sum of copies of Zp. A second factor, i.e., the group G2, is completed to a vector space over a field of fractions of a ring ZpA, in which case the field and the space are endowed with suitable topologies. The main result is giving a description of coordinate groups of irreducible algebraic sets over such a partially divisible topological group.
PubDate: 2016-12-01
DOI: 10.1007/s10469-016-9409-2

• A Generic relation on Recursively Enumerable Sets
• Authors: A. N. Rybalov
Abstract: We introduce the concept of a generic relation for algorithmic problems, which preserves the property of being decidable for a problem for almost all inputs and possesses the transitive property. As distinct from the classical m-reducibility relation, the generic relation under consideration does not possess the reflexive property: we construct an example of a recursively enumerable set that is generically incomparable with itself. We also give an example of a set that is complete with respect to the generic relation in the class of recursively enumerable sets.
PubDate: 2016-11-30
DOI: 10.1007/s10469-016-9410-9

• Sessions of the Seminar “Algebra i Logika”
• PubDate: 2016-11-10
DOI: 10.1007/s10469-016-9405-6

• On L. G. Kovàcs’ Problem
• Authors: A. V. Vasil’ev; S. V. Skresanov
PubDate: 2016-11-10
DOI: 10.1007/s10469-016-9404-7

• Layers over Minimal Logic
• Authors: L. L. Maksimova; V. F. Yun
Abstract: We introduce a classification of extensions of Johansson’s minimal logic J that extends the classification of superintuitionistic logics proposed by T. Hosoi. It is proved that the layer number of any finitely axiomatizable logic is effectively computable. Every layer over J has a least logic. It is stated that each layer has finitely many maximal logics, and minimal and maximal logics of all layers are recognizable over J.
PubDate: 2016-11-10
DOI: 10.1007/s10469-016-9399-0

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