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1.
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
2.
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
3.
4.
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
5.
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
6.
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
7.
N. Yu. Galanova 《Algebra and Logic》2003,42(1):14-19
Let
be a field of formal power series with real coefficients, whose supports are well ordered subsets of an Abelian group
of cardinality strictly less than
. For
, we give criteria of a section being symmetric and of a symmetric section being Dedekind. It is proved that an
-saturated non-standard real line
is isomorphic to some field of the form
. For
, some consequences are inferred regarding symmetric sections, and the cofinality of banks of the sections. 相似文献
8.
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
9.
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
10.
11.
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
12.
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
13.
We study positive semicharacters of generating Lie subsemigroup
of a connected Lie group
. These semicharacters are important for positive representations of
in Hilbert space and for completely monotonic functions in
. We describe the tangent map for a positive semicharacter and then obtain a necessary and sufficient condition for nontriviality of the wedge
consisting of all bounded positive semicharacters of
. In particular
is nontrivial for a solvable simply connected
and invariant
without nontrivial subgroups, but it is trivial for a semisimple
. 相似文献
14.
Peter V. Danchev 《Czechoslovak Mathematical Journal》2002,52(1):129-140
Suppose
is a commutative ring with identity of prime characteristic
and
is an arbitrary abelian
-group. In the present paper, a basic subgroup and a lower basic subgroup of the
-component
and of the factor-group
of the unit group
in the modular group algebra
are established, in the case when
is weakly perfect. Moreover, a lower basic subgroup and a basic subgroup of the normed
-component
and of the quotient group
are given when
is perfect and
is arbitrary whose
is
-divisible. These results extend and generalize a result due to Nachev (1996) published in Houston J. Math., when the ring
is perfect and
is
-primary. Some other applications in this direction are also obtained for the direct factor problem and for a kind of an arbitrary basic subgroup. 相似文献
15.
16.
17.
Let
and
be groups and let
be an extension of
by
. Given a property
of group compactifications, one can ask whether there exist compactifications
and
of N and K such that the universal
-compactification of G is canonically isomorphic to an extension of
by
. We prove a theorem which gives necessary and sufficient conditions for this to occur for general properties
and then apply this result to the almost periodic and weakly almost periodic compactifications of G. 相似文献
18.
Let
be a computable structure and let R be an additional relation on its domain. We establish a necessary and sufficient condition for the existence of an isomorphic copy
of
such that the image of R
is h-simple (h-immune) relative to
. 相似文献
19.
We deal with iterative algebras of functions of
-valued logic lacking projections, which we call algebras without projections. It is shown that a partially ordered set of algebras of functions of
-valued logic, for
, without projections contains an interval isomorphic to the lattice of all iterative algebras of functions of
-valued logic. It is found out that every algebra without projections is contained in some maximal algebra without projections, which is the stabilizer of a semigroup of non-surjective transformations of the basic set. It is proved that the stabilizer of a semigroup of all monotone non-surjective transformations of a linearly ordered 3-element set is not a maximal algebra without projections, but the stabilizer of a semigroup of all transformations preserving an arbitrary non one-element subset of the basic set is. 相似文献
20.
V. Yu. Popov 《Algebra and Logic》2005,44(1):46-54
There exist independently based semigroup varieties
and
,
, such that
has no cover in the interval [
;
].Translated from Algebra i Logika, Vol. 44, No. 1, pp. 81–96, January–February, 2005. 相似文献