Открытый доступ
Доступ предоставлен
Только для подписчиков
Том 56, № 6 (2018)
- Год: 2018
- Статей: 9
- URL: https://journal-vniispk.ru/0002-5232/issue/view/14546
Article
Structures Computable in Polynomial Time. II
Аннотация
We consider a new approach to investigating categoricity of structures computable in polynomial time. The approach is based on studying polynomially computable stable relations. It is shown that this categoricity is equivalent to the usual computable categoricity for computable Boolean algebras with computable set of atoms, and for computable linear orderings with computable set of adjacent pairs. Examples are constructed which show that this does not always hold. We establish a connection between dimensions based on computable and polynomially computable stable relations.
429-442
443-450
Pronormality of Hall Subgroups in Their Normal Closure
Аннотация
It is known that for any set π of prime numbers, the following assertions are equivalent: (1) in any finite group, π-Hall subgroups are conjugate; (2) in any finite group, π-Hall subgroups are pronormal. It is proved that (1) and (2) are equivalent also to the following: (3) in any finite group, π-Hall subgroups are pronormal in their normal closure. Previously [10, Quest. 18.32], the question was posed whether it is true that in a finite group, π-Hall subgroups are always pronormal in their normal closure. Recently, M. N. Nesterov [7] proved that assertion (3) and assertions (1) and (2) are equivalent for any finite set π. The fact that there exist examples of finite sets π and finite groups G such that G contains more than one conjugacy class of π-Hall subgroups gives a negative answer to the question mentioned. Our main result shows that the requirement of finiteness for π is unessential for (1), (2), and (3) to be equivalent.
451-457
Nonpresentability of Some Structures of Analysis in Hereditarily Finite Superstructures
Аннотация
It is proved that any countable consistent theory with infinite models has a Σ-presentable model of cardinality 2ω over ℍ????(ℝ). It is shown that some structures studied in analysis (in particular, a semigroup of continuous functions, certain structures of nonstandard analysis, and infinite-dimensional separable Hilbert spaces) have no simple Σ-presentations in hereditarily finite superstructures over existentially Steinitz structures. The results are proved by a unified method on the basis of a new general sufficient condition.
458-472
Polygons with a (P, 1)-Stable Theory
Аннотация
Polygons with a (P, 1)-stable theory are considered. A criterion of being (P, 1)-stable for a polygon is established. As a consequence of the main criterion we prove that a polygon SS, where S is a group, is (P, 1)-stable if and only if S is a finite group. It is shown that the class of all polygons with monoid S is (P, 1)-stable only if S is a one-element monoid. (P, 1)-stability criteria are presented for polygons over right and left zero monoids.
473-478
Locally Finite Suzuki–Higman 2-Groups
Аннотация
We prove the following theorem. Let U be a locally finite Suzuki–Higman 2-group with respect to an automorphism group H. Then U and H are representable as the respective unions of ascending chains of finite subgroups U1 < U2 < . . . < Un < . . . and H1 < H2 < . . . < Hn < . . ., in which case every subgroup Un is a Suzuki 2-group with respect to Hn.
479-497
Orders of Elements of Finite Almost Simple Groups
502-505
Sessions of the Seminar “Algebra i Logika”
506-507
Communications
The Number of Sylow Subgroups in Special Linear Groups of Degree 2
498-501