共查询到20条相似文献,搜索用时 15 毫秒
1.
Zvonimir Janko 《Archiv der Mathematik》2011,96(2):101-103
We prove here that a nonabelian finite p-group G has exactly one maximal subgroup with a noncyclic center if and only if Z(G) is cyclic and G has exactly one normal abelian subgroup of type (p, p). 相似文献
2.
3.
We classify here nonmetacyclic finite 2-groups all of whose nonmetacyclic subgroups are generated by involutions (Theorem
1.1). This solves problem Nr. 710 for p = 2 stated by Y. Berkovich in [1]. For p > 2 the corresponding problem is open.
Received: 14 March 2007 Revised: 15 April 2007 相似文献
4.
Zdravka Božikov 《Archiv der Mathematik》2006,86(1):11-15
According to a classical result of Burnside, if G is a finite 2-group, then the Frattini subgroup Φ(G) of G cannot be a nonabelian group of order 8. Here we study the next possible case, where G is a finite 2-group and Φ(G) is nonabelian of order 16. We show that in that case Φ(G) ≅ M × C2, where M ≅ D8 or M ≅ Q8 and we shall classify all such groups G (Theorem A).
Received: 16 February 2005; revised: 7 March 2005 相似文献
5.
S. S. Korobkov 《Russian Mathematics (Iz VUZ)》2011,55(6):46-52
We describe finite associative rings that contain at most two maximal subrings. 相似文献
6.
7.
P. P. Baryshovets 《Ukrainian Mathematical Journal》2006,58(5):685-693
We study groups G that satisfy the following conditions
(i) G is a finite solvable group with nonidentity primary metacyclic second commutator subgroup
(ii) all Sylow subgroups of G are elementary Abelian.
We describe the structure of groups of this type with complementable nonmetacyclic subgroups.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 5, pp. 607–615, May, 2006. 相似文献
8.
9.
10.
Zvonimir Janko 《Israel Journal of Mathematics》2006,154(1):157-184
We present an elementary proof of the classification theorem for finite nonmodular quaternion-free 2-groups. This proof does
not involve the structure theory of powerful 2-groups. Such a new proof is also necessary, since there are several gaps in
the original proof given in [5]. 相似文献
11.
12.
Joseph Kirtland 《Expositiones Mathematicae》2004,22(4):395-398
A finite separable metacyclic 2-group G can be written as the semidirect product of a cyclic group with another cyclic group. Necessary and sufficient conditions are given for when all other split decompositions of G result in, up to isomorphism, this same semidirect product representation for G. 相似文献
13.
Finite equilibrated 2-generated 2-groups 总被引:2,自引:0,他引:2
Gheorghe Silberberg 《Acta Mathematica Hungarica》2006,110(1-2):23-35
14.
B. M. Veretennikov 《Algebra and Logic》2011,50(3):226-244
An Alperin group is a group in which every 2-generated subgroup has a cyclic commutant. Previously, we constructed examples
of finite Alperin 2-groups with second commutant isomorphic to Z
2 or Z
4. Here, it is proved that for any natural n, there exists a finite Alperin 2-group whose second commutant is isomorphic to
Z
2n
. 相似文献
15.
Zvonimir Janko 《Mathematische Zeitschrift》2008,258(3):629-635
We determine here up to isomorphism the structure of any finite nonabelian 2-group G in which every two distinct maximal abelian subgroups have cyclic intersection. We obtain five infinite classes of such 2-groups
(Theorem 1.1). This solves for p = 2 the problem Nr. 521 stated by Berkovich (in preparation). The more general problem Nr. 258 stated by Berkovich (in preparation)
about the structure of finite nonabelian p-groups G such that A ∩ B = Z(G) for every two distinct maximal abelian subgroups A and B is treated in Theorems 3.1 and 3.2. In Corollary 3.3 we get a new result for an arbitrary finite 2-group. As an application
of Theorems 3.1 and 3.2, we solve for p = 2 a problem of Heineken-Mann (Problem Nr. 169 stated in Berkovich, in preparation), classifying finite 2-groups G such that A/Z(G) is cyclic for each maximal abelian subgroup A (Theorem 4.1).
相似文献
16.
The structure of finite groups in which every 3-maximal subgroup commutes with all maximal subgroups is described. 相似文献
17.
18.
19.
M. M. Gol'denberg 《Mathematical Notes》1971,10(2):515-520
A theorem is proved which classifies and describes up to generating elements and defining relations the finite 2-groups having invariant non-completely partitionable subgroups.Translated from Matematicheskie Zametki, Vol. 10, No. 2, pp. 151–161, August, 1971.The author is grateful to N. F. Sesekin for the problem statement and scientific direction. 相似文献
20.
John Sheehan 《Journal of Graph Theory》1977,1(1):37-43
Let h(n) be the largest integer such that there exists a graph with n vertices having exactly one Hamiltonian circuit and exactly h(n) edges. We prove that h(n) = [n2/4]+1 (n ≧ 4) and discuss some related problems. 相似文献