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1.
It is proved that a finite group isomorphic to a simple non-Abelian group L3(2m) or U3(2m) is, up to isomorphism, recognizable by a set of its element orders. On the other hand, for every simple group S=S4(2m), there exist infinitely many pairwise non-isomorphic groups G with w(G)=w(S). As a consequence, we present a list of all
recognizable finite simple groups G, for which 4t ∉ ω(G) with t>1.
Supported by RFFR grant No. 99-01-00550, by the National Natural Science Foundation of China (grant No. 19871066), and by
the State Education Ministry of China (grant No. 98083).
Translated fromAlgebra i Logika, Vol. 39, No. 5, pp. 567–585, September–October, 2000. 相似文献
2.
V. D. Mazurov 《Algebra and Logic》1997,36(1):23-32
For a finite group G, ω(G) denotes the set of orders of its elements. If ω is a subset of the set of natural numbers, h(ω)
stands for the number of pairwise nonisomorphic finite groups G for which ω(G)=ɛ. We prove that h(ω(G))=1, if G is isomorphic
to S9, S11, S12, S13, or A12, and h(ω(G))=2 if G is isomorphic to S2(6) or to O
8
+
(2). 01
Supported by RFFR grant No. 96-01-01893.
Translated fromAlgebra i Logika, Vol. 36, No. 1, pp. 37–53, January–February, 1997. 相似文献
3.
Let M be a simple group whose order is less than 108. In this paper, we prove that if G is a finite group with the same order and degree pattern as M, then the following statements hold: (a) If M ≠ A
10, U
4(2), then G ≅ M; (b) If M = A
10, then G ≅ A
10 or J
2 × ℤ3; (c) If M = U
4(2), then G is isomorphic to a 2-Frobenius group or U
4(2). In particular, all simple groups whose orders are less than 108 but A
10 and U
4(2) are OD-characterizable. As a consequence of this result, we can give a positive answer to a conjecture put forward by
W. J. Shi and J. X. Bi in 1990 [Lecture Notes in Mathematics, Vol. 1456, 171–180].
相似文献
4.
A. K. Shlyopkin 《Algebra and Logic》1999,38(1):51-66
A group G is saturated with groups in a set X if every finite subgroup of G is embeddable in G into a subgroup L isomorphic
to some group in X. We show that a Shunkov group has a periodic part if the saturating set for it coincides with one of the
following: {L2(q)}, {Sz(q)}, {Re(q)}, or {U3(2n)}.
Translated fromAlgebra i Logika, Vol. 38, No. 1, pp. 96–125, January–February, 1999. 相似文献
5.
Jia Feng Lü 《数学学报(英文版)》2009,25(6):1015-1030
The so-called weakly d-Koszul-type module is introduced and it turns out that each weakly d-Koszul-type module contains a d-Koszul-type submodule. It is proved that, M ∈ W H J^d(A) if and only if M admits a filtration of submodules: 0 belong to U0 belong to U1 belong to ... belong to Up = M such that all Ui/Ui-1 are d-Koszul-type modules, from which we obtain that the finitistic dimension conjecture holds in W H J^d(A) in a special case. Let M ∈ W H J^d(A). It is proved that the Koszul dual E(M) is Noetherian, Hopfian, of finite dimension in special cases, and E(M) ∈ gr0(E(A)). In particular, we show that M ∈ W H J^d(A) if and only if E(G(M)) ∈ gr0(E(A)), where G is the associated graded functor. 相似文献
6.
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
7.
Arrangements and cohomology 总被引:11,自引:0,他引:11
Michael Falk 《Annals of Combinatorics》1997,1(1):135-157
8.
Let X be a locally compact topological space and (X, E, Xω) be any triple consisting of a hyperfinite set X in a sufficiently saturated nonstandard universe, a monadic equivalence relation E on X, and an E-closed galactic set Xω ⊆ X, such that all internal subsets of Xω are relatively compact in the induced topology and X is homeomorphic to the quotient Xω/E. We will show that each regular complex Borel measure on X can be obtained by pushing down the Loeb measure induced by some internal function
. The construction gives rise to an isometric isomorphism of the Banach space M(X) of all regular complex Borel measures on X, normed by total variation, and the quotient
, for certain external subspaces
of the hyperfinite dimensional Banach space
, with the norm ‖f‖1 = ∑x ∈ X |f(x)|. If additionally X = G is a hyperfinite group, Xω = Gω is a galactic subgroup of G, E is the equivalence corresponding to a normal monadic subgroup G0 of Gω, and G is isomorphic to the locally compact group Gω/G0, then the above Banach space isomorphism preserves the convolution, as well, i.e., M(G) and
are isometrically isomorphic as Banach algebras.
Research of both authors supported by a grant by VEGA – Scientific Grant Agency of Slovak Republic. 相似文献
9.
V. D. Mazurov 《Algebra and Logic》2006,45(2):117-123
Let G be a group. A subset X of G is called an A-subset if X consists of elements of order 3, X is invariant in G, and every
two non-commuting members of X generate a subgroup isomorphic to A4 or to A5. Let X be the A-subset of G. Define a non-oriented graph Γ(X) with vertex set X in which two vertices are adjacent iff they
generate a subgroup isomorphic to A4. Theorem 1 states the following. Let X be a non-empty A-subset of G. (1) Suppose that C is a connected component of Γ(X)
and H = 〈C〉. If H ∩ X does not contain a pair of elements generating a subgroup isomorphic to A5 then H contains a normal elementary Abelian 2-subgroup of index 3 and a subgroup of order 3 which coincides with its centralizer
in H. In the opposite case, H is isomorphic to the alternating group A(I) for some (possibly infinite) set I, |I| ≥ 5. (2)
The subgroup 〈XG〉 is a direct product of subgroups 〈C
α〉-generated by some connected components C
α of Γ(X). Theorem 2 asserts the following. Let G be a group and X⊆G be a non-empty G-invariant set of elements of order 5 such that every two non-commuting members of X generate a subgroup
isomorphic to A5. Then 〈XG〉 is a direct product of groups each of which either is isomorphic to A5 or is cyclic of order 5.
Supported by RFBR grant No. 05-01-00797; FP “Universities of Russia,” grant No. UR.04.01.028; RF Ministry of Education Developmental
Program for Scientific Potential of the Higher School of Learning, project No. 511; Council for Grants (under RF President)
and State Aid of Fundamental Science Schools, project NSh-2069.2003.1.
__________
Translated from Algebra i Logika, Vol. 45, No. 2, pp. 203–214, March–April, 2006. 相似文献
10.
O. A. Alekseeva 《Algebra and Logic》2006,45(1):1-11
It is proved that if G is a finite group with an element order set as in the simple group 3D4(q), where q is even, then the commutant of G/F(G) is isomorphic to 3D4(q) and the factor group G/G′ is a cyclic {2, 3}-group.
__________
Translated from Algebra i Logika, Vol. 45, No. 1, pp. 3–19, January–February, 2006. 相似文献
11.
A. K. Shlyopkin 《Algebra and Logic》1998,37(5):345-350
A group G is saturated with groups of the set X if every finite subgroup K≤G is embedded in G into a subgroup L isomorphic
to some group of X. We study periodic conjugate biprimitive finite groups saturated with groups in the set {U3(2n)}. It is proved that every such group is isomorphic to a simple group U3(Q) over a locally finite field Q of characteristic 2.
Supported by the RF State Committee of Higher Education.
Translated fromAlgebra i Logika, Vol. 37, No. 5, pp. 606–615, September–October, 1998. 相似文献
12.
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
13.
Let X be a locally compact topological space and (X, E, Xω) be any triple consisting of a hyperfinite set X in a sufficiently saturated nonstandard universe, a monadic equivalence relation E on X, and an E-closed galactic set Xω ⊆ X, such that all internal subsets of Xω are relatively compact in the induced topology and X is homeomorphic to the quotient Xω/E. We will show that each regular complex Borel measure on X can be obtained by pushing down the Loeb measure induced by some internal function
X ? *\Bbb CX \rightarrow {}{^{\ast}{\Bbb C}}
. The construction gives rise to an isometric isomorphism of the Banach space M(X) of all regular complex Borel measures on X, normed by total variation, and the quotient
Mw(X)/M0(X){\cal M}_{\omega}(X)/{\cal M}_0(X)
, for certain external subspaces
M0(X), Mw(X){\cal M}_0(X), {\cal M}_{\omega}(X)
of the hyperfinite dimensional Banach space
*\Bbb CX{}{^{\ast}{\Bbb C}}^X
, with the norm ‖f‖1 = ∑x ∈ X |f(x)|. If additionally X = G is a hyperfinite group, Xω = Gω is a galactic subgroup of G, E is the equivalence corresponding to a normal monadic subgroup G0 of Gω, and G is isomorphic to the locally compact group Gω/G0, then the above Banach space isomorphism preserves the convolution, as well, i.e., M(G) and
Mw(G)/M0(G){\cal M}_{\omega}(G)/{\cal M}_0(G)
are isometrically isomorphic as Banach algebras. 相似文献
14.
For a domainU on a certaink-dimensional minimal submanifold ofS
n orH
n, we introduce a “modified volume”M(U) ofU and obtain an optimal isoperimetric inequality forU k
k
ω
k
M (D)
k-1
≤Vol(∂D)
k
, where ω
k
is the volume of the unit ball ofR
k
. Also, we prove that ifD is any domain on a minimal surface inS
+
n
(orH
n, respectively), thenD satisfies an isoperimetric inequality2π A≤L
2+A2 (2π A≤L2−A2 respectively). Moreover, we show that ifU is ak-dimensional minimal submanifold ofH
n, then(k−1) Vol(U)≤Vol(∂U).
Supported in part by KME and GARC 相似文献
15.
Let M be a quantizable symplectic manifold. If ψt is a loop in the group {Ham}(M) of Hamiltonian symplectomorphisms of M and A is a 2k-cycle in M, we define a symplectic action κA(ψ)∊ U(1) around ψt(A), which is invariant under deformations of ψ, and such that κA(ψ) depends only on the homology class of A. Using properties of κA( ) we determine a lower bound for ♯π1(Ham(O)), where O is a quantizable coadjoint orbit of a compact Lie group. In particular we prove that ♯π1(Ham(CPn)) ≥ n+1.
Mathematics Subject Classifications (2000): 53D05, 57S05, 57R17, 57T20. 相似文献
16.
17.
Let G be an abelian group, ε an anti-bicharacter of G and L a G-graded ε Lie algebra (color Lie algebra) over a field of characteristic zero. We prove that for all G-graded, positively filtered A such that the associated graded algebra is isomorphic to the G-graded ε-symmetric algebra S(L), there is a G- graded ε-Lie algebra L and a G-graded scalar two cocycle , such that A is isomorphic to U
ω
(L) the generalized enveloping algebra of L associated with ω. We also prove there is an isomorphism of graded spaces between the Hochschild cohomology of the generalized universal enveloping
algebra U(L) and the generalized cohomology of the color Lie algebra L.
Supported by the EC project Liegrits MCRTN 505078. 相似文献
18.
V. P. Burichenko 《Algebra and Logic》2008,47(6):384-394
Let G = SL(n, q), where q is odd, V be a natural module over G, and L = S2(V) be its symmetric square. We construct a 2-cohomology group H2(G, L). The group is one-dimensional over F
q if n = 2 and q ≠ 3, and also if (n, q) = (4, 3). In all other cases H2(G, L) = 0. Previously, such groups H2(G, L) were known for the cases where n = 2 or q = p is prime. We state that H2(G, L) are trivial for n ⩾ 3 and q = pm, m ⩾ 2. In proofs, use is made of rather elementary (noncohomological) methods.
__________
Translated from Algebra i Logika, Vol. 47, No. 6, pp. 687–704, November–December, 2008. 相似文献
19.
Young-Tak Oh 《Journal of Algebraic Combinatorics》2012,35(3):389-420
Let G be a group, U a subgroup of G of finite index, X a finite alphabet and q an indeterminate. In this paper, we study symmetric polynomials M
G
(X,U) and MGq(X,U)M_{G}^{q}(X,U) which were introduced as a group-theoretical generalization of necklace polynomials. Main results are to generalize identities
satisfied by necklace polynomials due to Metropolis and Rota in a bijective way, and to express MGq(X,U)M_{G}^{q}(X,U) in terms of M
G
(X,V)’s, where [V] ranges over a set of conjugacy classes of subgroups to which U is subconjugate. As a byproduct, we provide the explicit form of the GL
m
(ℂ)-module whose character is
M\mathbbZq(X,n\mathbbZ)M_{\mathbb{Z}}^{q}(X,n\mathbb{Z}), where m is the cardinality of X. 相似文献
20.
Let 1<q<∞, n(1−1/q)≤α<∞, 0<p<∞ and ω1,ω2 ɛA
1(R
n
) (the Muckenhoupt class). In this paper, the author introduce the weighted Herz-type Hardy spaces hk
q
α,p
(gw1,ω2) and present their atomic decomposition. Using the atomic decomposition, the author find out their dual spaces, establish
the boundedness on these spaces of the pseudo-differential operators of order zero and show thatD(R
n
), the class of C∞(Rn)-functions with compactly support, is dense inhK
q
α,p
(ω1,ω2) and there is a subsequence, which converges in distrbutional sense to some distribution ofhK
q
α,p
(ω1,ω2), of any bounded sequence inhK
q
α,p
(ω1,ω2). In addition, the author also set up the boundedness of some non-linear quantities in compensated compactness.
Supported by the NECF and the NECF and the NNSF of China. 相似文献