Открытый доступ
Доступ предоставлен
Только для подписчиков
Том 55, № 5 (2016)
- Год: 2016
- Статей: 10
- URL: https://journal-vniispk.ru/0002-5232/issue/view/14539
Article
Abnormality Criteria for p-Complements
Аннотация
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.
347-353
Spectra of Automorphic Extensions of Finite Simple Exceptional Groups of Lie Type
Аннотация
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 E6 or E7. 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.
354-366
Levi Decomposition for Carpet Subgroups of Chevalley Groups Over a Field
Аннотация
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 Φi of Φ. The obtained result can be viewed as an analog of the Levi decomposition.
367-375
Partially Divisible Completions of Rigid Metabelian Pro-p-groups
Аннотация
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.
376-386
A Generic relation on Recursively Enumerable Sets
Аннотация
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.
387-393
394-402
Permutation Groups in Categorical Additive Horn Theories
407-411
Supergeneric Equations
412-418
Sessions of the Seminar “Algebra i Logika”
419-420
Communications
The Centralizer Dimension of Generalized Baumslag–Solitar Groups
403-406