共查询到20条相似文献,搜索用时 15 毫秒
1.
V. I. Chaadaev 《Siberian Mathematical Journal》1971,12(1):148-153
2.
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
3.
4.
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
5.
6.
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
7.
Gemma Parmeggiani 《Rendiconti del Circolo Matematico di Palermo》1995,44(2):215-238
In this paper we investigate the class of finite soluble groups in which every subnormal subgroup has normal normalizer. In
particular we prove that they areUN
2U, whereU andN
2denote finite abelian groups and of finite nilpotent groups of class at most 2 respectively. 相似文献
8.
9.
We describe groupsG in which the set {abc, acb, bac, bca, cab, cba} contains three different elements at most for anya, b, c ∈G and show how this type of problem is connected with the rewritability (or permutation) properties of groups. 相似文献
10.
11.
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
12.
Let
\mathfrakX{\mathfrak{X}} be a class of groups. A group G is called a minimal non-
\mathfrakX{\mathfrak{X}}-group if it is not an
\mathfrakX{\mathfrak{X}}-group but all of whose proper subgroups are
\mathfrakX{\mathfrak{X}}-groups. In [16], Xu proved that if G is a soluble minimal non-Baer-group, then G/G
′′ is a minimal non-nilpotent-group which possesses a maximal subgroup. In the present note, we prove that if G is a soluble minimal non-(finite-by-Baer)-group, then for all integer n ≥ 2, G/γ
n
(G′) is a minimal non-(finite-by-abelian)-group. 相似文献
13.
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
14.
15.
Finite 2-groups with exactly one nonmetacyclic maximal subgroup 总被引:1,自引:1,他引:0
Zvonimir Janko 《Israel Journal of Mathematics》2008,166(1):313-347
We determine here the structure of the title groups. All such groups G will be given in terms of generators and relations, and many important subgroups of these groups will be described. Let d(G) be the minimal number of generators of G. We have here d(G) ≤ 3 and if d(G) = 3, then G′ is elementary abelian of order at most 4. Suppose d(G) = 2. Then G′ is abelian of rank ≤ 2 and G/G′ is abelian of type (2, 2m), m ≥ 2. If G′ has no cyclic subgroup of index 2, then m = 2. If G′ is noncyclic and G/Φ(G 0) has no normal elementary abelian subgroup of order 8, then G′ has a cyclic subgroup of index 2 and m = 2. But the most important result is that for all such groups (with d(G) = 2) we have G = AB, for suitable cyclic subgroups A and B. Conversely, if G = AB is a finite nonmetacyclic 2-group, where A and B are cyclic, then G has exactly one nonmetacyclic maximal subgroup. Hence, in this paper the nonmetacyclic 2-groups which are products of two cyclic subgroups are completely determined. This solves a long-standing problem studied from 1953 to 1956 by B. Huppert, N. Itô and A. Ohara. Note that if G = AB is a finite p-group, p > 2, where A and B are cyclic, then G is necessarily metacyclic (Huppert [4]). Hence, we have solved here problem Nr. 776 from Berkovich [1]. 相似文献
16.
17.
I. A. Ivanov-Pogodaev 《Journal of Mathematical Sciences》2008,152(2):191-202
This work presents a sample construction of an algebra with the ideal of relations defined by a finite Gröbner basis for which the question whether this element is a zero divisor is algorithmically unsolvable. This gives the negative answer to a question raised by V. N. Latyshev. 相似文献
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19.
Katarína Cechlrov 《Linear algebra and its applications》2000,310(1-3):123-128
For unsolvable systems of linear equations of the form Ax=b over the max–min (fuzzy) algebra we propose an efficient method for finding a Chebychev-best approximation of the matrix
in the set . 相似文献
20.
We give a manageable sufficient condition for indecomposability of Butler \(\mathrm B (n)\) -groups, allowing the easy construction of a big family of indecomposable torsionfree Abelian groups of finite rank. 相似文献