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1.
It is proved that every group of the form G = AB with subgroups A and B each of which has a cyclic subgroup of index at most 2 is metacyclicby-finite.
Received: 13 July 2007 相似文献
2.
Finite groups G=AB factorized by two subgroups A and B such that every subgroup of A permutes with every subgroup of B are studied in this paper. The behaviour of such products with respect to the class of finite groups in which Sylow-permutability is transitive is analyzed. 相似文献
3.
Let H and K be normal subgroups of a finite group G and let K≤H. If A is a subgroup of G such that AH=AK or A∩H=A∩K, we say that A covers or avoids H/K respectively. The purpose of this paper is to investigate factor groups of a finite group G using this concept. We get some characterizations of a finite group being solvable or supersolvable and generalize some known results. 相似文献
4.
A subgroup H of G is said to be $\pi$-quasinormal in G if it
permute with every Sylow subgroup of G.
In this paper, we extend the study on the structure of a finite group under the
assumption that some subgroups of G are
$\pi$-quasinormal in G. The main result we proved
in this paper is the following:Theorem 3.4.
Let ${\cal F}$ be a saturated formation
containing the supersolvable groups. Suppose that G is a group with a
normal subgroup H such that $G/H \in {\cal F}$,
and all maximal subgroups of any Sylow subgroup of $F^{*}(H)$ are $\pi$-quasinormal in
G, then $G \in {\cal F}$.
Received: 10 May 2002 相似文献
5.
A subgroup H of a finite group
G is called c-normal in
G if there exists a normal subgroup
N of G such that
G = HN and $H \cap N \leq H_{G} = {\rm core}_{G}(H)$. In this paper, we investigate the class of groups
of which every maximal subgroup of its Sylow
p-subgroup is c-normal and the
class of groups of which some minimal subgroups of its Sylow
p-subgroup is c-normal for some prime number
p. Some interesting results are obtained and
consequently, many known results related to
p-nilpotent groups and
p-supersolvable groups are generalized. 相似文献
6.
《Quaestiones Mathematicae》2013,36(1):103-120
AbstractWe characterize Abelian groups with a minimal generating set: Let τ A denote the maximal torsion subgroup of A. An infinitely generated Abelian group A of cardinality κ has a minimal generating set iff at least one of the following conditions is satisfied:
dim(A/pA) = dim(A/qA) = κ for at least two different primes p, q.
dim(t A/pt A) = κ for some prime number p.
Σ{dim(A/(pA + B)) ∣ dim(A/(pA + B)) < κ} = κ for every finitely generated subgroup B of A.
7.
《Quaestiones Mathematicae》2013,36(1-2):59-82
Abstract This paper is devoted to the study of groups with the property that the Frattini factor group is a T-group, i.e. a group in which every subnormal subgroup is normal. We give necessary and suffucient conditions for a direct product G = H x K of finite groups H and K to have such a property. Some structure theorems are also discussed. 相似文献
8.
We consider the product AB of two finite mutually permutable subgroups A, B and find some subnormal subgroups of the product. This leads to local and otherwise generalized statements about products of supersolvable groups.Received: 19 May 2004 相似文献
9.
Let G = AB be the mutually permutable product of the subgroups A and B. It is shown that if A and B are contained in a Fitting class
, then the commutator subgroup G′ of G is also contained in
.
Received: 14 August 2006 Revised: 17 September 2006 相似文献
10.
A. R. Chekhlov 《Algebra and Logic》2009,48(4):298-308
A ring is said to be normal if all of its idempotents are central. It is proved that a mixed group A with a normal endomorphism ring contains a pure fully invariant subgroup G ⊕ B, the endomorphism ring of a group G is commutative, and a subgroup B is not always distinguished by a direct summand in A. We describe separable, coperiodic, and other groups with normal endomorphism rings. Also we consider Abelian groups in which
the square of the Lie bracket of any two endomorphisms is the zero endomorphism. It is proved that every central invariant
subgroup of a group is fully invariant iff the endomorphism ring of the group is commutative. 相似文献
11.
A subgroup of a finite group G is said to be S-quasinormal in G if it permutes with every Sylow subgroup of G. In this paper we give a characterization of a finite group G under the assumption that every subgroup of the generalized Fitting subgroup of prime order is S-quasinormal in G. 相似文献
12.
In a finite group G every element can be factorized in such a way that there is one factor for each prime divisor p of | G |, and the order of this factor is pα for some integer α ≧ 0. We define g ∈G to be uniquely factorizable if it has just one such factorization (whose factors must be pairwise commuting). We consider the existence of uniquely factorizable
elements and its relation to the solvability of the group. We prove that G is solvable if and only if the set of all uniquely factorizable elements of G is the Fitting subgroup of G. We also prove various sufficient conditions for the non-existence of uniquely factorizable elements in non-solvable groups.
Received: 9 June 2005 相似文献
13.
Nobuyuki Kemoto 《Topology and its Applications》2007,154(3):758-770
Let A and B be subspaces of an ordinal. It is proved that the product A×B is countably paracompact if and only if it is rectangular. Before this main result, we discuss several covering properties of products with one ordinal factor. In particular, for every paracompact space X, it is proved that the product X×A is paracompact if so is A. 相似文献
14.
M. M. Semko 《Ukrainian Mathematical Journal》1998,50(11):1750-1754
We introduce the notion of a CDN(]-group G, namely, a group such that, for any pair of its subgroups A and B such that A is a proper nonmaximal subgroup of B, there exists a normal subgroup N of G and A < N ≤ B. Thirteen types of non-Dedekind nilpotent groups and 9 types of nonnilpotent locally graded groups of this kind are described.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 11, pp. 1532–1536, November, 1998. 相似文献
15.
Let R be a ring and G a group. An R-module A is said to be minimax if A includes a noetherian submodule B such that A/B is artinian. The authors study a ?G-module A such that A/C A (H) is minimax (as a ?-module) for every proper not finitely generated subgroup H. 相似文献
16.
It is known that in a finite solvable group G, a subgroup H is abnormal if and only if every subgroup of G containing H is self-normalizing in G. Although, in general, the assumption of solvability cannot be dropped, in this paper we prove the theorem for the special case G = An and H a second maximal intransitive subgroup of An.Received: 1 July 2003 相似文献
17.
In this paper we define a degenerateC
F-set in PG (2,q
2) as the set of points of intersection of corresponding lines under a suitable collineation between two pencils of lines with
vertices two distinct pointsA andB mapping the lineA ∨B onto itself. We prove that every such a set is the union of the lineA ∨B and a Baer subplane and vice versa every Baer subplane can be seen as a subset of a degenerateC
F-set. 相似文献
18.
We consider an almost hyper-Abellan group G of a finite Abelian sectional rank that is the product of two subgroups A and B. We prove that every subgroup H that belongs to the intersection A ∩ B and is ascending both in A and B is also an ascending subgroup in the group G. We also show that, in the general case, this statement is not true.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 6, pp. 842–848, June, 1997. 相似文献
19.
We prove conditions for a product of distinct subgroups of an arbitrary group G to be a subgroup of G. In particular, the normal closure of any A ≤ G is equal to the product of some distinct conjugates of A. As an application of the later result we derive constraints on the size of a nontrivial conjugacy class of a finite non-Abelian simple group. 相似文献
20.
《代数通讯》2013,41(12):4741-4752
Abstract Subgroups A and B of a finite group are said to be 𝒩-connected if the subgroup generated by elements x and y is a nilpotent group, for every pair of elements x in A and y in B. The behaviour of finite pairwise permutable and 𝒩-connected products are studied with respect to certain classes of groups including those groups where all the subnormal subgroups permute with all the maximal subgroups, the so-called SM-groups, and also the class of soluble groups where all the subnormal subgroups permute with all the Carter subgroups, the so-called C-groups. 相似文献