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1.
Il'ya Ponomarenko 《Journal of Mathematical Sciences》1997,85(1):1722-1726
Let G be a primitive permutation group of order |G| and degree n. Then |G|≤ndm, where d is the minimal size of a nontrivial orbit of a one-point stabilizer of G and m is the minimal degree of a nonprincipal
irreducible representation of G entering its permutation representation. Bibliography: 8 titles.
Dedicated to L. D. Faddeev on occasion of his 60th birthday
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 215, 1994, pp. 256–263.
Translated by I. Ponomarenko. 相似文献
2.
It is well known that the number of isolated singular points of a hypersurface of degree d in ℂPm does not exceed the Arnol’d number Am(d), which is defined in combinatorial terms. In the paper it is proved that if b
m−1
±
(d) are the inertia indices of the intersection form of a nonsingular hypersurface of degree d in ℂPm, then the inequality Am(d)<min{b
m−1
+
(d), b
m−1
−
(d)} holds if and only if (m−5)(d−2)≥18 and (m,d)≠(7,12). The table of the Arnol’d numbers for 3≤m≤14, 3≤d≤17 and for 3≤m≤14,
d=18, 19 is given. Bibliography: 6 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 180–190.
Translated by O. A. Ivanov and N. Yu. Netsvetev. 相似文献
3.
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
4.
A. I. Sozutov 《Algebra and Logic》2007,46(3):195-199
An involution j of a group G is said to be almost perfect in G if any two involutions in jG whose product has infinite order are conjugated by a suitable involution in jG. Let G contain an almost perfect involution j and |CG(j)| < ∞. Then the following statements hold: (1) [j,G] is contained in an FC-radical of G, and |G: [j,G]| ⩽ |CG(j)|; (2) the commutant of an FC-radical of G is finite; (3) FC(G) contains a normal nilpotent class 2 subgroup of finite
index in G.
__________
Translated from Algebra i Logika, Vol. 46, No. 3, pp. 360–368, May–June, 2007. 相似文献
5.
I. S. Ponizovskii 《Journal of Mathematical Sciences》1990,52(3):3170-3178
The semigroup algebras over a field K of the semigroups Tn of all permutations of a set of n elements are considered. It is proved: if n≤3 and (n!)-1∈ K then the algebra KTn has a finite representation type. Also the finiteness of the representation type of the semigroup algebra KS is established,
where S is the sub-semigroup of Tn (n is arbitrary) such that S=Jn∪G where Jn={x∈Tn|rank x=1}, while G is a doubly transitive subgroup of the symmetric group Sn, the order of G being invertible in K.
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR,
Vol. 160, pp. 229–238, 1987. 相似文献
6.
A. K. Shlyopkin 《Algebra and Logic》1998,37(2):127-138
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 biprimitive finite groups saturated with groups of the sets {L2(pn)}, {Re(32n+1)}, and {Sz(22n+1)}. It is proved thai such groups are all isomorphic to {L2(P)}, {Re(Q)}, or {Sr(Q)} over locally finite fields.
Supported by the RF State Committee of Higher Education.
Translated fromAlgebra i Logika, Vol. 37, No. 2, pp. 224–245, March–April, 1998. 相似文献
7.
A connected, finite two-dimensional CW-complex with fundamental group isomorphic toG is called a [G, 2]
f
-complex. LetL⊲G be a normal subgroup ofG. L has weightk if and only ifk is the smallest integer such that there exists {l
1,…,l
k}⊆L such thatL is the normal closure inG of {l
1,…,l
k}. We prove that a [G, 2]
f
-complexX may be embedded as a subcomplex of an aspherical complexY=X∪{e
1
2
,…,e
k
2
} if and only ifG has a normal subgroupL of weightk such thatH=G/L is at most two-dimensional and defG=defH+k. Also, ifX is anon-aspherical [G, 2]
f
-subcomplex of an aspherical 2-complex, then there exists a non-trivial superperfect normal subgroupP such thatG/P has cohomological dimension ≤2. In this case, any torsion inG must be inP. 相似文献
8.
Dan Segal 《Israel Journal of Mathematics》1996,94(1):7-19
A groupG hasweak polynomial subgroup growth (wPSG) of degree ≤α if each finite quotient Ḡ ofG contains at most │Ḡ│
a
subgroups. The main result is that wPSG of degree α implies polynomial subgroup growth (PSG) of degree at mostf(α). It follows that wPSG is equivalent to PSG. A corollary is that if, in a profinite groupG, thek-generator subgroups have positive “density” δ, thenG is finitely generated (the number of generators being bounded by a function ofk and δ). 相似文献
9.
N. N. Kushpel 《Journal of Mathematical Sciences》2006,136(3):3957-3965
A linear group G ≤ GL(V) is called same-invariant if the subspace of linear invariants Vg is one and the same for all g ∈ G, g ≠ 1. In this paper, we consider finite same-invariant linear groups of orders pq, (p,
q) = 1, or p2 over a field of characteristic p. Bibliography: 8 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 321, 2005, pp. 224–239. 相似文献
10.
N. A. Vavilov 《Journal of Mathematical Sciences》2007,147(5):6995-7004
11.
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
12.
《代数通讯》2013,41(8):3263-3279
Abstract We study the problem concerning the influence of the index of maximal subgroup or the degree of primitive permutation representation of the finite simple groups on the structure of a group. Let G be a finite group and s be the index of maximal subgroup of the Monster M. In this paper, we prove that there exists an epimorphism from G to M or A s if G has the primitive permutation representation of degree s, and as a consequence we prove that the Monster is determined by every s. 相似文献
13.
In §2, we prove that if a 2-group G and all its nonabelian maximal sub-groups are two-generator, then G is either metacyclic or minimal non-abelian. In §3, we consider a similar question for p > 2. In §4 the 2-groups all of whose minimal nonabelian subgroups have order 16 and a cyclic subgroup of index 2, are classified.
It is proved, in §5, that if G is a nonmetacyclic two-generator 2-group and A, B, C are all its maximal subgroups with d(A) ≤ d(B) ≤ d(C), then d(C) = 3 and either d(A) = d(B) = 3 (this occurs if and only if G/G′ has no cyclic subgroup of index 2) or else d(A) = d(B) = 2. Some information on the last case is obtained in Theorem 5.3. 相似文献
14.
On the ball |x| ≤ 1 of R
m
, m ≥ 2, a radial variational problem, related to a priori estimates for solutions to extremal elliptic equations with fixed
ellipticity constant α
is investigated. Such a problem has been studied and solved [see Manselli Ann. Mat. Pura Appl. (IV), t. LXXXIX:31–54, 1971]
in L
p
spaces, with p ≤ m. In this paper, we assume p > m and we prove the existence of a positive number α
0 = α
0(p,m) such that if there exists a smooth function maximizing the problem, whose representation is explicitly determined as in Manselli [Ann.
Mat. Pura Appl. (IV), t. LXXXIX:31–54, 1971] This fact is no longer true if 0 < α < α
0.
相似文献
15.
A. V. Vasilyev 《Algebra and Logic》1997,36(5):302-310
A minimal permutation representation of a group is its faithful permutation representation of least degree. We will find degrees
and point stabilizers, as well as ranks, subdegrees, and double stabilizers, for groups of types E6, E7, and E8. This brings to a close the study of minimal permutation representations of finite simple Chevalley groups.
Supported by RFFR grant No. 93-01-01501, through the program “Universities of Russia,” and by grant No. RPC300 of ISF and
the Government of Russia.
Translated fromAlgebra i Logika, Vol. 36, No. 5, pp. 518–530, September–October, 1997. 相似文献
16.
S. A. Nazarov 《Journal of Mathematical Sciences》2008,152(5):674-689
For the linear theory of water waves, we find out families of submerged or surface-piercing bodies in an infinite three-dimensional
canal, which depend on a small parameter ε > 0 and have the following property: for any positive d and natural J, there exists
ε(d, J) > 0 such that, for ε ∈ (0, ε(d, J)], the segment [0, d] of the continuous spectrum of the problem contains at least
J eigenvalues. These eigenvalues are associated with trapped modes, i.e., solutions of the homogeneous problem, which decay
exponentially at infinity and possess finite energy. Bibliography: 27 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 348, 2007, pp. 98–126. 相似文献
17.
Let G be a permutation group on a set Ω with no fixed points in,and m be a positive integer.Then the movement of G is defined as move(G):=sup Γ {|Γg\Γ| | g ∈ G}.It was shown by Praeger that if move(G) = m,then |Ω| 3m + t-1,where t is the number of G-orbits on.In this paper,all intransitive permutation groups with degree 3m+t-1 which have maximum bound are classified.Indeed,a positive answer to her question that whether the upper bound |Ω| = 3m + t-1 for |Ω| is sharp for every t > 1 is given. 相似文献
18.
A. V. Vasilyev 《Algebra and Logic》1996,35(6):371-383
A minimal permutation representation of a group is a faithful permutation representation of least degree. Well-studied to
date are the minimal permutation representations of finite sporadic and classical groups for which degrees, point stabilizers,
as well as ranks, subdegrees, and double stabilizers, have been found. Here we attempt to provide a similar account for finite
simple ezceptional groups of types G2 and F4.
Supported by RFFR grant No. 96-01-01893, the program “Universities of Russia,” and by International Science Foundation and
Government of Russia grant No. RPC300.
Translated fromAlgebra i Logika, Vol. 35, No. 6, pp. 663–684, November–December, 1996. 相似文献
19.
Guido Zappa 《Annali di Matematica Pura ed Applicata》1962,57(1):211-219
Sunto. Hughes ha avanzato la seguente congettura: se G è un gruppo, p un numero primo, e Hp il sottogruppo generato dagli elementi di G che non hanno periodo p, si presenta uno dei tre casi seguenti: Hp=1; Hp=G; [G: Hp]=p. Vari autori hanno provato l'esattezza di tale congettura per larghe classi di gruppi. In questa Nota si dimostra che
tale congettura è esatta per i p-gruppi finiti in cui ogni sottogruppo generato da tre elementi, due dei quali di periodo
p, abbia classe ≤p; essa è quindi esatta in particolare per i p-gruppi di classe ≤p.
A Enrico Bompiani in occasione del suo Giubileo scientifico. 相似文献
Summary Hughes advanced the following conjecture: “let G be a group, p a prime and Hp the subgroup generated by elements of G having order p; then Hp=1 or Hp=G or [G: Hp]=p„. Several authors have proved this conjecture for various classes of groups. The Author proves Hughes conjecture for finite p-groups such that every subgroup {x 1 , x 2, y} generated by two elements x 1 , x 2 having order p, and by a thirth element y, has class ≤p; in particular, the conjecture is proved for finite p-groups having class ≤p.
A Enrico Bompiani in occasione del suo Giubileo scientifico. 相似文献
20.
Paolo Emilio Ricci 《Rendiconti del Circolo Matematico di Palermo》1992,41(2):185-196
A representation formula in terms of Lucas polynomials of the second kind in several variables (see formula (4.3)), for the
sum rulesJ
s
(i)
introduced by K.M. Case [1] and studied by J.S. Dehesa et al. [2]–[3] in order to obtain informations about the zeros’ distribution
of eigenfunctions of a class of ordinary polynomial differential operator, is derived.
Lavoro eseguito nell’ambito del G.N.I.M. del C.N.R. 相似文献