共查询到20条相似文献,搜索用时 15 毫秒
1.
Abstract. – We construct a finitely presented non-amenable group without free non-cyclic subgroups thus providing a finitely
presented counterexample to von Neumann’s problem. Our group is an extension of a group of finite exponent n ≫ 1 by a cyclic group, so it satisfies the identity [x,y]
n
= 1.
Manuscrit reĉu le 8 février 2001.
RID="*"
ID="*"Both authors were supported in part by the NSF grant DMS 0072307. In addition, the research of the first author was
supported in part by the Russian Fund for Basic Research 99-01-00894 and by the INTAS grant, the research of the second author
was supported in part by the NSF grant DMS 9978802. 相似文献
2.
Evija Ribnere 《Monatshefte für Mathematik》2009,48(2):387-401
There are two sequences in two variables which characterize the solvability of finite groups. Namely, the sequence of Bandman,
Greuel, Grunewald, Kunyavskii, Pfister and Plotkin which is defined by u
1 = x
−2
y
−1
x and un=[x un-1-1 x-1, yun-1-1 y-1]{u_{n}=[x u_{n-1}^{-1} x^{-1}, yu_{n-1}^{-1} y^{-1}] } and the sequence of Bray, Wilson, and Wilson defined by s
1 = x and sn=[sn-1 -y, sn-1]{s_{n}=[s_{n-1} ^{-y}, s_{n-1}] }. We define new sequences and proof that six of them characterize the solvability of finite groups. 相似文献
3.
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.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 351, 2007, pp. 242–252. 相似文献
4.
A. I. Budkin 《Algebra and Logic》2007,46(4):219-230
Let Lq(qG) be the quasivariety lattice contained in a quasivariety generated by a group G. It is proved that if G is a finitely
generated torsion-free group in
(i.e., G is an extension of an Abelian group by a group of exponent 2n), which is a split extension of an Abelian group by a cyclic group, then the lattice Lq(qG) is a finite chain.
__________
Translated from Algebra i Logika, Vol. 46, No. 4, pp. 407–427, July–August, 2007. 相似文献
5.
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
6.
We revisit old conjectures of Fermat and Euler regarding the representation of integers by binary quadratic form x 2+5y 2. Making use of Ramanujan’s 1 ψ 1 summation formula, we establish a new Lambert series identity for $\sum_{n,m=-\infty }^{\infty}q^{n^{2}+5m^{2}}We revisit old conjectures of Fermat and Euler regarding the representation of integers by binary quadratic form x
2+5y
2. Making use of Ramanujan’s 1
ψ
1 summation formula, we establish a new Lambert series identity for
?n,m=-¥¥qn2+5m2\sum_{n,m=-\infty }^{\infty}q^{n^{2}+5m^{2}}
. Conjectures of Fermat and Euler are shown to follow easily from this new formula. But we do not stop there. Employing various
formulas found in Ramanujan’s notebooks and using a bit of ingenuity, we obtain a collection of new Lambert series for certain
infinite products associated with quadratic forms such as x
2+6y
2, 2x
2+3y
2, x
2+15y
2, 3x
2+5y
2, x
2+27y
2, x
2+5(y
2+z
2+w
2), 5x
2+y
2+z
2+w
2. In the process, we find many new multiplicative eta-quotients and determine their coefficients. 相似文献
7.
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
8.
E. A. Kireeva 《Journal of Mathematical Sciences》2008,152(4):540-557
Let F be a field of prime characteristic p and let V
p be the variety of associative algebras over F without unity defined by the identities [[x, y], z] = 0 and x
4 = 0 if p = 2 and by the identities [[x, y], z] = 0 and x
p = 0 if p > 2 (here [x, y] = xy − yx). Let A/V
p be the free algebra of countable rank of the variety V
p and let S be the T-space in A/V
p generated by x
12
x
22 ⋯ x
k2 + V
2, where k ∈ ℕ if p = 2, and by {ie4170-01}, where k ∈ ℕ and α
1, …, α
2k
∈ {0, p − 1} if p > 2. As is known, S is not finitely generated as a T-space. In the present paper, we prove that S is a limit T-space, i.e., a maximal nonfinitely generated T-space. As a corollary, we have constructed a limit T-space in
the free associative F-algebra without unity of countable rank.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 1, pp. 135–159, 2007. 相似文献
9.
V. M. Kaplitsky 《Journal of Mathematical Sciences》2010,165(4):455-462
We study sufficient conditions for exponential decay at infinity for eigenfunctions of a class of integral equations in unbounded
domains in ℝ
n
. We consider integral operators K whose kernels have the form
k( x,y ) = c( x,y )\frace - a| x - y || x - y |b , ( x,y ) ? W×W, k\left( {x,y} \right) = c\left( {x,y} \right)\frac{{{e^{ - \alpha \left| {x - y} \right|}}}}{{{{\left| {x - y} \right|}^\beta }}},\,\left( {x,y} \right) \in \Omega \times \Omega, 相似文献
10.
Let Π n d denote the space of all spherical polynomials of degree at most n on the unit sphere $\mathbb{S}^{d}
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