共查询到20条相似文献,搜索用时 31 毫秒
1.
N. S. Romanovskii 《Algebra and Logic》2008,47(6):426-434
A soluble group G is rigid if it contains a normal series of the form G = G1 > G2 > … > Gp > Gp+1 = 1, whose quotients Gi/Gi+1 are Abelian and are torsion-free as right ℤ[G/Gi]-modules. The concept of a rigid group appeared in studying algebraic geometry over groups that are close to free soluble.
In the class of all rigid groups, we distinguish divisible groups the elements of whose quotients Gi/Gi+1 are divisible by any elements of respective groups rings Z[G/Gi]. It is reasonable to suppose that algebraic geometry over divisible rigid groups is rather well structured. Abstract properties
of such groups are investigated. It is proved that in every divisible rigid group H that contains G as a subgroup, there is
a minimal divisible subgroup including G, which we call a divisible closure of G in H. Among divisible closures of G are divisible
completions of G that are distinguished by some natural condition. It is shown that a divisible completion is defined uniquely
up to G-isomorphism.
Supported by the Council for Grants (under RF President) and State Aid of Leading Scientific Schools (grant NSh-344.2008.1).
Translated from Algebra i Logika, Vol. 47, No. 6, pp. 762–776, November–December, 2008. 相似文献
2.
Spectra of finite linear and unitary groups 总被引:1,自引:0,他引:1
A. A. Buturlakin 《Algebra and Logic》2008,47(2):91-99
The spectrum of a finite group is the set of its element orders. An arithmetic criterion determining whether a given natural
number belongs to a spectrum of a given group is furnished for all finite special, projective general, and projective special
linear and unitary groups.
Supported by RFBR (grant Nos. 08-01-00322 and 06-01-39001) and by the Council for Grants (under RF President) and State Aid
of Leading Scientific Schools (project NSh-344.2008.1).
__________
Translated from Algebra i Logika, Vol. 47, No. 2, pp. 157–173, March–April, 2008. 相似文献
3.
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
4.
A. N. Starkov 《Mathematical Notes》1998,63(2):233-241
A criterion for a wide class of topological groups which includes linear discrete groups and Lie groups to be Tychonoff groups
is established. The main result provides a criterion for an almost polycyclic group to have the Tychonoff property. By the
well-known Tits alternative, this yields the required criterion for linear discrete groups. In conclusion it is pointed out
that a particular case of the presented proof yields a Tychonoff property criterion for Lie groups. In addition, an example
of a polycyclic group without Tychonoff subgroups of finite index is constructed.
Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 269–279, February, 1998.
The author wishes to express his gratitude to R. I. Grigorchuk for setting the problem and his interest in the work.
This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-00182 and by the American Mathematical
Society Fund. 相似文献
5.
E. I. Timoshenko 《Algebra and Logic》2006,45(4):254-260
It is proved that test rank of a free solvable non-Abelian group of finite rank is 1 less than the rank of that group. This
gives the answer to Question 14.88 posed in the Kourovka Notebook by Fine and Shpilrain, asking whether or not a free solvable
group of rank 2 and solvability index n ≥ 3 has test elements.
Supported by RFBR grant No. 05-01-00292.
__________
Translated from Algebra i Logika, Vol. 45, No. 4, pp. 447–457, July–August, 2006. 相似文献
6.
Orderable solvable groups in which every relatively convex subgroup is normal are studied. If such a class is subgroup closed
than it is precisely the class of solvable orderable groups which are locally of finite (Mal’tsev) rank. A criterion for an
orderable metabelian group to have every relatively convex subgroup normal is given. Examples of an orderable solvable group
G of length three with periodic G/G′ and of an orderable solvable group of length four with only one proper normal relatively convex subgroup are constructed.
To the memory of N. Ya. Medvedev
Supported by RFBR (project No. 03-01-00320).
Translated from Algebra i Logika, Vol. 48, No. 3, pp. 291–308, May–June, 2009. 相似文献
7.
V. M. Kopytov 《Algebra and Logic》1998,37(3):170-180
We construct an example of a fully orderable group that is not locally solvable. It is also shown that a free group is embedded
in a fully orderable group. To meet these ends, use is made of a group of invertible formal power series with zero free term
under composition.
Supported by RFFR grant No. 96-01-00088.
Translated fromAlgebra i Logika, Vol. 37, No. 3, pp. 301–319, May–June, 1998. 相似文献
8.
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.
__________
Translated from Algebra i Logika, Vol. 47, No. 3, pp. 288–306, May–June, 2008. 相似文献
9.
Non-nilpotent, finitely generated, associative nil-algebras are studied as well as their adjoint groups and Golod groups.
Solutions are given to some problems in residually finite group theory, questions posed in the Kourovka Notebook included.
Supported by RFBR grant No. 03-01-00356.
__________
Translated from Algebra i Logika, Vol. 45, No. 2, pp. 231–238, March–April, 2006. 相似文献
10.
A. S. Kondratev 《Siberian Mathematical Journal》2007,48(6):1001-1018
We prove that if L is one of the simple groups E
6(q) and 2
E
6(q) and G is some finite group with the same spectrum as L, then the commutant of G/F(G) is isomorphic to L and the quotient G/G′ is a cyclic {2,3}-group.
Original Russian Text Copyright ? 2007 Kondrat’ev A. S.
The author was supported by the Russian Foundation for Basic Research (Grant 04-01-00463) and the RFBR-NSFC (Grant 05-01-39000).
__________
Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 6, pp. 1250–1271, November–December, 2007. 相似文献
11.
S. A. Zyubin 《Algebra and Logic》2006,45(5):296-305
A subgroup having non-empty intersection with each class of conjugate elements of the group is said to be conjugately dense.
It is shown that, under certain conditions, the number of conjugately dense subgroups in a free product with amalgamation
is not less than some cardinal. As a consequence, P. Neumann’s conjecture in the Kourovka notebook (Question 6.38) is refuted.
It is also stated that a modular group and a non-Abelian group of countable or finite rank possess continuum many pairwise
non-conjugate conjugately dense subgroups.
Supported by RFBR grant No. 03-01-00905.
__________
Translated from Algebra i Logika, Vol. 45, No. 5, pp. 520–537, September–October, 2006. 相似文献
12.
B. A. F. Wehrfritz 《Central European Journal of Mathematics》2007,5(3):596-606
Let G be a hypercentral group. Our main result here is that if G/G’ is divisible by finite then G itself is divisible by finite. This extends a recent result of Heng, Duan and Chen [2], who prove in a slightly weaker form
the special case where G is also a p-group. If G is torsion-free, then G is actually divisible.
相似文献
13.
V. A. Roman'kov 《Algebra and Logic》2007,46(1):37-45
It is proved that in any finite representation of any finitely generated nilpotent group of nilpotency class l ⩾ 1, the averaged
Dehn function σ(n) is subasymptotic w.r.t. the function nl+1. As a consequence it is stated that in every finite representation of a free nilpotent group of nilpotency class l of finite
rank r ⩾ 2, the Dehn function σ(n) is Gromov subasymptotic.
Supported by RFBR grant No. 04-01-00489.
__________
Translated from Algebra i Logika, Vol. 46, No. 1, pp. 60–74, January–February, 2007. 相似文献
14.
N. S. Romanovskii 《Algebra and Logic》2007,46(4):274-280
The research launched in [1] is brought to a close by examining algebraic sets in a metabelian group G in two important cases:
(1) G = Fn is a free metabelian group of rank n; (2) G = Wn,k is a wreath product of free Abelian groups of ranks n and k.
Supported by RFBR grant No. 05-01-00292.
__________
Translated from Algebra i Logika, Vol. 46, No. 4, pp. 503–513, July–August, 2007. 相似文献
15.
It is proved that if L is one of the simple groups 3D4(q) or F4(q), where q is odd, and G is a finite group with the set of element orders as in L, then the derived subgroup of G/F(G) is
isomorphic to L and the factor group G/G′ is a cyclic {2, 3}-group.
__________
Translated from Algebra i Logika, Vol. 44, No. 5, pp. 517–539, September–October, 2005.
Supported by RFBR grant No. 04-01-00463. 相似文献
16.
A number of conditions are specified which are sufficient for totally ordered groups with polycyclic factor group to contain
a finite normal series of convex subgroups whose factors possess good enough properties. In any case studying such totally
ordered groups is reduced to treating extensions of these groups as well as their virtually o-equivalent extensions. The concept
of a virtually o-equivalent extension is a particular case of the notion of an Archimedean extension.
Supported by RFBR project No. 03-01-00320.
Translated from Algebra i Logika, Vol. 47, No. 5, pp. 529–540, September–October, 2008. 相似文献
17.
I. A. Dolguntseva 《Algebra and Logic》2007,46(6):373-384
We introduce the concept of Hochschild cohomologies for associative conformal algebras. It is shown that the second cohomology
group of a conformal Weyl algebra with values in any bimodule is trivial. As a consequence, we derive that the conformal Weyl
algebra is segregated in any extension with nilpotent kernel.
Supported by RFBR grant No. 05-01-00230 and via SB RAS Integration project No. 1.9.
__________
Translated from Algebra i Logika, Vol. 46, No. 6, pp. 688–706, November–December, 2007. 相似文献
18.
A. V. Zavarnitsin 《Algebra and Logic》2006,45(2):106-116
An exhaustive solution is given to the recognition-by-spectrum problem for finite, simple, three-dimensional unitary groups.
For every such group, the number of non-isomorphic, finite, isospectral groups is determined. In particular, a new counterexample
to Problem 13.63 in the Kourovka Notebook is furnished.
Supported by RFBR grant No. 05-01-00797, and by SB RAS Young Researchers Support grant No. 29 and Integration Project No.
2006.1.2.
__________
Translated from Algebra i Logika, Vol. 45, No. 2, pp. 185–202, March–April, 2006. 相似文献
19.
D. O. Revin 《Algebra and Logic》2008,47(3):210-227
20.
Maximal tori of all finite simple classical groups, as well as of special and general projective linear and unitary groups,
are treated. For every such torus, its expression as a direct sum of cyclic groups is obtained in an explicit form.
Supported by RFBR grant Nos. 05-01-00797 and 06-01-39001, and by SB RAS Integration Project No. 2006.1.2.
__________
Translated from Algebra i Logika, Vol. 46, No. 2, pp. 129–156, March–April, 2007. 相似文献