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1.
2.
A. I. Budkin 《Algebra and Logic》2000,39(6):363-369
Let
be a class of all groups G for which the normal closure (x)
G
of every element x belongs to a class
.
is a Levi class generated by
. Let
and
0 be classes of finitely generated nilpotent groups and of torsion-free, finitely generated, nilpotent groups, respectively. We prove that
and
, and so
and
. It is shown that quasivarieties
and
are closed under free products, and that each contains at most one maximal proper subquasivariety. It is also proved that
is closed under free products if so is
. 相似文献
3.
A. M. Protopopov 《Algebra and Logic》2003,42(4):279-286
We study into the question of whether a partial order can be induced from a partially right-ordered group
onto a space
of right cosets of
w.r.t. some subgroup
of
. Examples are constructed showing that the condition of being convex for
in
is insufficient for this. A necessary and sufficient condition (in terms of a subgroup
and a positive cone
of
) is specified under which an order of
can be induced onto
. Sufficient conditions are also given. We establish properties of the class of partially right-ordered groups
for which
is partially ordered for every convex subgroup
, and properties of the class of groups such that
is partially ordered for every partial right order
on
and every subgroup
that is convex under
. 相似文献
4.
吴启光 《应用数学学报(英文版)》1995,11(4):378-388
QUADRATICESTIMATORSOFQUADRATICFUNCTIONSWITHPARAMETERSINNORMALLINEARMODELS¥WUQIGUANG(吴启光)(InstituteofSystemeScience,theChinese... 相似文献
5.
A. A. Bulatov 《Algebra and Logic》1994,33(5):287-306
The lattice
of clones of functions over a k-element set is studied. It is shown that every lattice which is a countable direct product of finite lattices is embedded (up to isomorphism) in
and, hence, in
for k 4. This directly implies that every finite and any countable residually finite lattice is embedded in
, k 4, and that no nontrivial quasi-identity holds in
, k 4. A number of particular lattices (which are free in some lattice varieties) embeddable in
, k 4,are presented.
Translated fromAlgebra i Logika, Vol. 33, No. 5, pp. 514–549, September–October, 1994. 相似文献
6.
An automorphism
of a group X is said to be quadratic if there exist integers
and
such that
for any
. If
is a Frobenius group then an element
is said to be quadratic if
induces, by conjugation in the core of
, a quadratic automorphism. By definition, a group H acts on a group F freely if
for
and
only with
or
. It is proved that a Frobenius group generated by two quadratic elements is finite and its core is commutative. In particular, any Frobenius group generated by two elements of order at most 4 is finite. Also we argue that a Frobenius group with finitely generated soluble core is finite. The results mentioned are used to show that a group
acting freely on an Abelian group is finite if it is generated by elements of order 3, and the order of a product of every two elements of order 3 in
is finite. 相似文献
7.
Superlocals in Symmetric and Alternating Groups 总被引:1,自引:0,他引:1
D. O. Revin 《Algebra and Logic》2003,42(3):192-206
On Aschbacher's definition, a subgroup N of a finite group
is called a
-superlocal for a prime
if
. We describe the
-superlocals in symmetric and alternating groups, thereby resolving part way Problem 11.3 in the Kourovka Notebook [3]. 相似文献
8.
If a regular graph of valence
and diameter
has
vertices, then
, which was proved by Moore (cf. [1]). Graphs for which this non-strict inequality turns into an equality are called Moore graphs. Such have an odd girth equal to
. The simplest example of a Moore graph is furnished by a
-triangle. Damerell proved that a Moore graph of valence
has diameter 2. In this case
, the graph is strongly regular with
and
, and the valence
is equal to 3 (Peterson's graph), to 7 (Hoffman–Singleton's graph), or to 57. The first two graphs are of rank 3. Whether a Moore graph of valence
exists is not known; yet, Aschbacher proved that the Moore graph with
will not be a rank 3 graph. We call the Moore graph with
the Aschbacher graph. Cameron showed that such cannot be vertex transitive. Here, we treat subgraphs of fixed points of Moore graph automorphisms and an automorphism group of the hypothetical Aschbacher graph for the case where that group contains an involution. 相似文献
9.
D. M. Smirnov 《Algebra and Logic》2003,42(2):136-146
We continue to study interrelations between permutative varieties and the cyclic varieties defined by cycles of the form
. A criterion is given determining whether a cyclic variety
is interpretable in
. For a permutation
without fixed elements, it is stated that a set of primes
for which
is interpretable in
in the lattice
is finite. It is also proved that for distinct primes
, the Helly number of a type
in
coincides with dimension of the dual type
and equals
. 相似文献
10.
We prove a theorem on possible test rank values for groups of the form
. It is shown that test rank of a free polynilpotent group
is equal to
or
, for any
and every collection
of classes. Moreover,
for
and
. 相似文献
11.
B. P. Paneah 《Functional Analysis and Its Applications》2003,37(1):46-60
In this paper, some solvability problems for functional equations of the form
are studied. Here I is a finite closed interval in , F is an unknown continuous function,
and
are given continuous maps of I into itself, and
, and
are real-valued continuous functions on I. Such equations are of interest not only by themselves as an object of analysis, but they are also a necessary link in solving various problems in such diverse fields as integral and functional equations, measure theory, and boundary problems for hyperbolic differential equations. The major part of the proofs is based on the new results in the theory of dynamical systems generated by a noncommutative semigroup with two generators. 相似文献
12.
V. Yu. Popov 《Algebra and Logic》2001,40(1):55-66
It is proved that there exists an infinite sequence of finitely based semigroup varieties
such that, for all i, an equational theory for
and for the class
of all finite semigroups in
is undecidable while an equational theory for
and for the class
of all finite semigroups in
is decidable. An infinite sequence of finitely based semigroup varieties
is constructed so that, for all i, an equational theory for
and for the class
of all finite semigroups in
is decidable whicle an equational theory for
and for the class
of all finite semigroups in
is not. 相似文献
13.
D. M. Smirnov 《Algebra and Logic》2004,43(4):249-257
For integers 1 m < n, a Cantor variety with m basic n-ary operations i and n basic m-ary operations k is a variety of algebras defined by identities k(1(
), ... , m(
)) =
k and i(1(
), ... ,n(
)) = y
i, where
= (x
1., ... , x
n) and
= (y
1, ... , y
m). We prove that interpretability types of Cantor varieties form a distributive lattice, , which is dual to the direct product 1 × 2 of a lattice, 1, of positive integers respecting the natural linear ordering and a lattice, 2, of positive integers with divisibility. The lattice is an upper subsemilattice of the lattice
of all interpretability types of varieties of algebras. 相似文献
14.
S. Yu. Podzorov 《Algebra and Logic》2003,42(2):121-129
S. Goncharov and S. Badaev showed that for
, there exist infinite families whose Rogers semilattices contain ideals without minimal elements. In this connection, the question was posed as to whether there are examples of families that lack this property. We answer this question in the negative. It is proved that independently of a family chosen, the class of semilattices that are principal ideals of the Rogers semilattice of that family is rather wide: it includes both a factor lattice of the lattice of recursively enumerable sets modulo finite sets and a family of initial segments in the semilattice of
-degrees generated by immune sets. 相似文献
15.
D. M. Smirnov 《Algebra and Logic》2005,44(2):109-116
Let be the set of all primes,
the field of all algebraic numbers, and Z the set of square-free natural numbers. We consider partially ordered sets of interpretability types such as
, and
, where AD is a variety of -divisible Abelian groups with unique taking of the pth root p(x) for every p ,
is a variety of
-modules over a normal field
, contained in
, and Gn is a variety of n-groupoids defined by a cyclic permutation (12 ...n). We prove that
, and
are distributive lattices, with
and
where
ub and
ubf are lattices (w.r.t. inclusion) of all subsets of the set and of finite subsets of , respectively.Deceased.__________Translated from Algebra i Logika, Vol. 44, No. 2, pp. 198–210, March–April, 2005. 相似文献
16.
In this paper we study the relationship between one-sided reverse Holder classes
and the
classes. We find the best possible range of
to which an
weight belongs, in terms of the
constant. Conversely, we also find the best range of
to which a
weight belongs, in terms of the
constant. Similar problems for
,
and
are solved using factorization. 相似文献
17.
V. F. Murzina 《Algebra and Logic》2003,42(3):181-191
A modal logic associated with the
-spaces introduced by Ershov is examined. We construct a modal calculus that is complete w.r.t. the class of all strictly linearly ordered
-frames, and the class of all strictly linearly ordered
-frames. 相似文献
18.
19.
O. V. Bogopol'skii 《Algebra and Logic》2001,40(1):17-33
Let be a compact connected surface with basepoint x and H
1 and H
2 be two finitely generated subgroups of 1(, x) on finite sets of generators. It is proved that there exists an algorithm which decides whether there is an automorphism
for which (H
1) = H
2, and if so, it finds such. 相似文献