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1.
We consider locally nilpotent periodic groups admitting an almost regular automorphism of order 4. The following are results
are proved: (1) If a locally nilpotent periodic group G admits an automorphism ϕ of order 4 having exactly m<∞ fixed points,
then (a) the subgroup {ie176-1} contains a subgroup of m-bounded index in {ie176-2} which is nilpotent of m-bounded class,
and (b) the group G contains a subgroup V of m-bounded index such that the subgroup {ie176-3} is nilpotent of m-bounded class
(Theorem 1); (2) If a locally nilpotent periodic group G admits an automorphism ϕ of order 4 having exactly m<∞ fixed points,
then it contains a subgroup V of m-bounded index such that, for some m-bounded number f(m), the subgroup {ie176-4}, generated
by all f(m) th powers of elements in {ie176-5} is nilpotent of class ≤3 (Theorem 2).
Supported by RFFR grant No. 94-01-00048 and by ISF grant NQ7000.
Translated fromAlgebra i Logika, Vol. 35, No. 3, pp. 314–333, May–June, 1996. 相似文献
2.
Let {ie166-01} be a set of finite groups. A group G is said to be saturated by the groups in {ie166-02} if every finite subgroup
of G is contained in a subgroup isomorphic to a member of {ie166-03}. It is proved that a periodic group G saturated by groups
in a set {U3(2m) | m = 1, 2, …} is isomorphic to U3(Q) for some locally finite field Q of characteristic 2; in particular, G is locally finite.
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Translated from Algebra i Logika, Vol. 47, No. 3, pp. 288–306, May–June, 2008. 相似文献
3.
N. S. Romanovskii 《Algebra and Logic》1999,38(3):193-201
Denote byB a class of solvable groups having a finite normal series with torsion-free Abelian factors, and by % MathType!MTEF!2!1!+-%
feaafiart1ev1aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC% vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wz% ZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbb%
L8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpe% pae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaam% aaeaqbaaGcbaWefv3ySLgzgjxyRrxDYbqehuuDJXwAKbIrYf2A0vNC%
aGGbaiqb-fa8czaaraaaaa!475E!\[\bar \mathfrak{B}\] a class of groups every finitely generated subgroup of which is approximated
by {ie193-3}. We prove that if {ie193-4} is a free product with relations of groups A1,…,An in the class {ie193-5}, where n>m and all relations are taken from the Cartesian subgroups, then there exist distinct indices
i1,…,in-m such that gp(Ai1,…,Ain-m)=Ai1 *…* Ain-m. A similar fact is established for solvable products with relations.
Supported by RFFR grant No. 99-01-00567.
Translated fromAlgebra i Logika, Vol. 38, No. 3, pp. 354–367, May–June, 1999. 相似文献
4.
A. I. Budkin 《Algebra and Logic》2008,47(5):304-313
Let A be a universal algebra and H its subalgebra. The dominion of H in A (in a class {ie304-01}) is the set of all elements
a ∈ A such that every pair of homomorphisms f, g: A → ∈ {ie304-02} satisfies the following: if f and g coincide on H, then
f(a) = g(a). A dominion is a closure operator on a set of subalgebras of a given algebra. The present account treats of closed
subalgebras, i.e., those subalgebras H whose dominions coincide with H. We introduce projective properties of quasivarieties
which are similar to the projective Beth properties dealt with in nonclassical logics, and provide a characterization of closed
algebras in the language of the new properties. It is also proved that in every quasivariety of torsion-free nilpotent groups
of class at most 2, a divisible Abelian subgroup H is closed in each group 〈H, a〉 generated by one element modulo H.
Translated from Algebra i Logika, Vol. 47, No. 5, pp. 541–557, September–October, 2008. 相似文献
5.
D. A. Anikeeva 《Journal of Mathematical Sciences》2008,152(6):817-825
Let ξ(t), t ∈ [0, 1], be a tempered stable process. By {ie4447-01} we denote the law of ξ in the Skorokhod space {ie4447-02}.
For the measure {ie4447-03}, we construct the group of nonsingular transformations of {ie4447-04}. Bibliography: 10 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 351, 2007, pp. 38–53. 相似文献
6.
N. V. Smorodina 《Journal of Mathematical Sciences》2008,152(6):934-940
Let ξ(t), t ∈ [0, 1], be an α-stable Lévy process in ℝd. Denote by {ie4563-01} the measure generated by ξ in the Skorokhod space {ie4563-02}. Under some conditions on the spectral
measure of the process ξ, we construct a group of {ie4563-03}-preserving transformations of {ie4563-04}. Bibliography: 12
titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 351, 2007, pp. 242–252. 相似文献
7.
V. K. Kharchenko 《Algebra and Logic》1996,35(1):49-58
Let L be a finite-dimensional differential Lie algebra acting on a prime ring R and let the inner part {ie49-1} of L be quasi-Frobenius.
Then a constant ring RL is prime iff {ie49-2} is a differentially simple ring. A ring of constants is semiprime iff {ie49-3} is a direct sum of differentially
simple rings, and the prime dimension of a constant ring is equal to the number of differentially simple summands {ie49-4}.
The Galois closure of L is obtained from L by adding all the inner derivations of a symmetric Martindale quotient ring which
agree with elements from {ie49-5}.
Supported by RFFR grant No. 93-01-16171 and by ISF grant RPS000-RPS300.
Translated fromAlgebra i Logika, Vol. 35, No. 1, pp. 88–104, January–February, 1996. 相似文献
8.
V. V. Savchuk 《Ukrainian Mathematical Journal》2008,60(6):910-926
We construct a linear method {ie910-01} for the approximation (in the unit disk) of classes of holomorphic functions {ie910-02}
that are the Hadamard convolutions of the unit balls of the Bergman space A
p
with reproducing kernels {ie910-03}. We give conditions for ψ under which the method {ie910-04} approximates the class {ie910-05}
in the metrics of the Hardy space H
s
and the Bergman space A
s
, 1 ≤ s ≤ p, with an error that coincides in order with the value of the best approximation by algebraic polynomials.
Translated from in Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 6, pp. 783–795, June, 2008. 相似文献
9.
Yu. L. Ershov 《Algebra and Logic》2008,47(3):155-165
The basic result of the paper is the main theorem worded as follows. Let {ie155-01} be a valued field such that {ie155-02}
has characteristic p > 0 and let {ie155-03} be an extension of valued fields satisfying the following conditions: (i) there exists a set {ie155-04} for which {ie155-05} is a separating transcendence basis for a field {ie155-06} over FR; (ii) Γ
R is p-pure in {ie155-07}, i.e., {ie155-08} does not contain elements of order p; (iii) there exists a set B1 ⊂ F0× such that the family {ie155-09} is linearly independent in the elementary p-group {ie155-10}; (iv) F0 is algebraic over F(B0 ⋃ B1). Then the property of being stable for {ie155-11} implies being stable for {ie155-12}.
Supported by the Council for Grants (under RF President) and State Aid of Leading Scientific Schools (grant NSh-344.2008.1)
and by RFBR (grant No. 08-01-00442-a).
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Translated from Algebra i Logika, Vol. 47, No. 3, pp. 269–287, May–June, 2008. 相似文献
10.
IfL
n(x) is thenth Laguerre polynomial and {ie45-1}, then we can expand the functions {ie45-2} over (0, ∞) in terms of the set {ie45-3}, i.e.,
{ie45-4}. In this paper we prove, an old-standing conjecture that (−1)
tKrt>0 for 0≦t≦r (r=0,1,…); i.e., that, in the sense defined by Trench, the set {ie45-5} is alternating with respect to the set {ie45-6}. 相似文献
11.
Let R be a finitely generated algebra over a field of characteristic 0 with a locally nilpotent derivation δ ≠ 0. We show that if {ie313-1}, where the invariants {ie313-2} are prime and satisfy a polynomial identity, then {ie313-3}. Furthermore, when R is a domain, the same conclusion holds without the assumption that R is finitely generated. This enables us to obtain a result on skew polynomial rings. These results extend work of Bell and Smoktunowicz on domains with GK dimension in the interval [2, 3). 相似文献
12.
We study Σ-definability of countable models over hereditarily finite {ie193-01} superstructures over the field ℝ of reals, the field
ℂ of complex numbers, and over the skew field ℍ of quaternions. In particular, it is shown that each at most countable structure
of a finite signature, which is Σ-definable over {ie193-02} with at most countable equivalence classes and without parameters, has a computable isomorphic
copy. Moreover, if we lift the requirement on the cardinalities of the classes in a definition then such a model can have
an arbitrary hyperarithmetical complexity, but it will be hyperarithmetical in any case. Also it is proved that any countable
structure Σ-definable over {ie193-03}, possibly with parameters, has a computable isomorphic copy and that being Σ-definable over {ie193-04} is equivalent to being Σ-definable over {ie193-05}.
Supported by RFBR-DFG, grant No. 06-01-04002 DFGa.
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Translated from Algebra i Logika, Vol. 47, No. 3, pp. 335–363, May–June, 2008. 相似文献
13.
E. G. Kir’yatskiĭ 《Siberian Mathematical Journal》2010,51(1):48-52
Considering the class {ie48-01} of analytic functions {ie48-02} in the unit disk with a
m,n
ε ℝ and the nonvanishing nth divided difference [F(z);z
0, ⋯, z
n
] for all z
0, ℝ, z
n ∈ E we establish that {ie48-03}, where {ie48-04}. If n is an odd number then {ie48-05}. 相似文献
14.
S. A. Gurchenkov 《Algebra and Logic》1996,35(3):149-159
We deal with varieties of lattice-ordered groups {ie149-1} defined by the identity [xn, yn]=e. The structure of subdirectly indecomposable l-groups in the variety {ie149-2} is studied, and we establish that l-varieties
satisfying the identity [xn, yn]=e and generated by a finitely generated l-group are finitely based. It is shown that l-varieties {ie149-3} with finite axiomatic
rank {ie149-4} also have finite bases of identities.
Translated fromAlgebra i Logika, Vol. 35, No. 3, pp. 268–287, May–June, 1996. 相似文献
15.
Summary We study embeddings between torsion-free nilpotent groups having isomorphic localizations. Firstly, we show that for finitely
generated torsion-free nilpotent groups of nilpotency class 2, the property of having isomorphicP-localizations (whereP denotes any set of primes) is equivalent to the existence of mutual embeddings of finite index not divisible by any prime
inP. We then focus on a certain family Γ of nilpotent groups whose Mislin genera can be identified with quotient sets of ideal
class groups in quadratic fields. We show that the multiplication of equivalence classes of groups in Γ induced by the ideal
class group structure can be described by means of certain pull-back diagrams reflecting the existence of enough embeddings
between members of each Mislin genus. In this sense, the family Γ resembles the family N0 of infinite, finitely generated nilpotent groups with finite commutator subgroup. We also show that, in further analogy with
N0, two groups in Γ with isomorphic localizations at every prime have isomorphic localizations at every finite set of primes.
We supply counterexamples showing that this is not true in general, neither for finitely generated torsion-free nilpotent
groups of class 2 nor for torsion-free abelian groups of finite rank.
Supported by DGICYT grant PB94-0725
This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag. 相似文献
16.
D. O. Revin 《Algebra and Logic》2008,47(3):210-227
17.
We observe an unknown function of d variables ƒ(t), t ∈ [0, 1]d, in the white Gaussian noise of level ε > 0. We assume that {ie4526-01}, where {ie4526-02} is a ball in the Hilbert space
{ie4526-03} of tensor product structure. Under minimax setup, we consider two problems: estimate ƒ (for quadratic losses)
and detect ƒ, i.e., test the null hypothesis H0: ƒ = 0 against the alternatives {ie4526-04}. We are interested in the case {ie4526-05}. We study sharp, rate, and log-asymptotics
(as ε → 0 and d → ∞) in the problems. In particular, we show that log-asymptotics are essentially different for d ≪ log ε−1 and d ≫ log ε−1. Bibliography: 19 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 351, 2007, pp. 180–218. 相似文献
18.
S. Norvidas 《Lithuanian Mathematical Journal》2008,48(4):427-437
For σ > 0, the Bernstein space {ie427-01} consists of those L
1(ℝ) functions whose Fourier transforms are supported by [−σ, σ]. Since {ie427-02} is separable and dual to some Banach space, the closed unit ball {ie427-03} of {ie427-04} has sufficiently
large sets of both exposed and strongly exposed points: {ie427-05} coincides with the closed convex hull of its strongly exposed
points. We investigate some properties of exposed points, construct several examples, and obtain as corollaries relations
between the sets of exposed, strongly exposed, weak* exposed, and weak* strongly exposed points of {ie427-06}. 相似文献
19.
This paper is devoted to a class of homogeneous left invariant operators L\ on the nilpotent Lie group G^{d+2} of the form
$L-\lambda=-\sum\limits_{j=1}^d X_j^2-i\sum\limits_{m=1}^2 \lambda _m T_m,\lambda=\lambda_1,\lambda_2)\in C^2$
where {X_1,\cdots ,X_d,T_1, T_2} is a base of left invariant vector fields on G^{d+2}. With aid of harmonic analysis on nilpotent Lie groups and the method of increment operators, for all admissible L_\lambda, subelliptic estimate and an explicit inverse axe given and the hypoellipticity and the global solvability are obtained. Also, the structure of the set of admissible points \lambda is described exhaustively. 相似文献
20.
A non-nilpotent finite group whose proper subgroups are all nilpotent is called a Schmidt group. A subgroup A is said to be
seminormal in a group G if there exists a subgroup B such that G = AB and AB1 is a proper subgroup of G, for every proper subgroup B1 of B. Groups that contain seminormal Schmidt subgroups of even order are considered. In particular, we prove that a finite
group is solvable if all Schmidt {2, 3}-subgroups and all 5-closed {2, 5}-Schmidt subgroups of the group are seminormal; the
classification of finite groups is not used in so doing. Examples of groups are furnished which show that no one of the requirements
imposed on the groups is unnecessary.
Supported by BelFBR grant Nos. F05-341 and F06MS-017.
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Translated from Algebra i Logika, Vol. 46, No. 4, pp. 448–458, July–August, 2007. 相似文献