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Том 56, № 4 (2017)
- Год: 2017
- Статей: 10
- URL: https://journal-vniispk.ru/0002-5232/issue/view/14544
Article
Automorphism Groups of Small Distance-Regular Graphs
Аннотация
We consider undirected graphs without loops and multiple edges. Previously, V. P. Burichenko and A. A. Makhnev [1] found intersection arrays of distance-regular locally cyclic graphs with the number of vertices at most 1000. It is shown that the automorphism group of a graph with intersection array {15, 12, 1; 1, 2, 15}, {35, 32, 1; 1, 2, 35}, {39, 36, 1; 1, 2, 39}, or {42, 39, 1; 1, 3, 42} (such a graph enters the above-mentioned list) acts intransitively on the set of its vertices.
261-268
Automorphism Groups of Diagonal Zp-Forms of the Lie Algebra sl2(Qp), p > 2
Аннотация
It follows from [2] that two nondiagonal forms like S(n, d) + ZpA and S(n, d) + ZpA′ are isomorphic if the elements of A and A′ are conjugated via the group \( {\mathrm{Aut}}_{{\boldsymbol{Z}}_p}S\left(n,d\right) \). In the present paper, we settle just this question on conjugation. In other words, we describe the group \( {\mathrm{Aut}}_{{\boldsymbol{Z}}_p}S\left(n,d\right) \) and clarify under which conditions two elements of S(n, d) are conjugate under the action of this group on S(n, d), p > 2.
269-280
Algebraic Geometry Over Algebraic Structures. VI. Geometrical Equivalence
Аннотация
The present paper is one in our series of works on algebraic geometry over arbitrary algebraic structures, which focuses on the concept of geometrical equivalence. This concept signifies that for two geometrically equivalent algebraic structures \( \mathcal{A} \) and ℬ of a language L, the classification problems for algebraic sets over \( \mathcal{A} \) and ℬ are equivalent. We establish a connection between geometrical equivalence and quasiequational equivalence.
281-294
295-301
Reducibility of Computable Metrics on the Real Line
Аннотация
We study computable reducibility of computable metrics on R induced by reducibility of their respective Cauchy representations. It is proved that this ordering has a subordering isomorphic to an arbitrary countable tree. Also we introduce a weak version of computable reducibility and construct a countable antichain of computable metrics that are incomparable with respect to it. Informally, copies of the real line equipped with these metrics are pairwise homeomorphic but not computably homeomorphic.
302-317
Fragments of Functional Clones
Аннотация
In [1] we came up with some approach and problems associated with subsets of functional clones on a fixed set that consist of functions occurring in a clone with a fixed restriction on their arity. This approach receives further development.
318-323
P-Stable Polygons
Аннотация
P-stable polygons are studied. It is proved that the property of being (P, s)-, (P, a)-, and (P, e)-stable for the class of all polygons over a monoid S is equivalent to S being a group. We describe the structure of (P, s)-, (P, a)-, and (P, e)-stable polygons SA over a countable left zero monoid S and, under the condition that the set A \ SA is indiscernible, over a right zero monoid.
324-336
Universal Generalized Computable Numberings and Hyperimmunity
Аннотация
Generalized computable numberings relative to hyperimmune and high oracles are studied. We give a description of oracles relative to which every finite computable family has a universal computable numbering. Also we present a characterization of the class of oracles relative to which every universal computable numbering of an arbitrary finite family is precomplete, and establish a sufficient condition for universal generalized computable numberings to be precomplete. In addition, we look into the question on limitedness of universal numberings computable relative to high oracles.
337-347
Sessions of the Seminar “Algebra i Logika”
353-354
Communications
Elementary Equivalence of Partially Commutative Lie Rings and Algebras
348-352