Maximal commutative subalgebras of functions on spaces dual to Lie algebras

The problem of searching the maximal commutative sets of polynomial functions on the dual space to the semidirect sum of a Lie algebra and a vector space is studied. It is proved that if the first component of the semi-direct sum is a compact algebra, then the set of functions can be described explicitly. This result is applied to some particular Lie algebras.     

Semidirect products OF fuzzy subgroups

The semidirect product of two groups is an important construction in group theory. In this paper we define the semidirect product of fuzzy subgroups and give conditions for it to be a fuzzy subgroup. This extends the work of H. Sherwood on direct products of fuzzy subgroups. We then give an example where a fuzzy subgroup of a semidirect product is a semidirect product of fuzzy subgroups.     

On two classes of finite inseparable p-groups

A finite group is inseparable,it does not split over any proper nontrivial normal subgroup;that is,if it has no nontrivial semidirect product decompositions.This paper investigates two classes of finite inseparable p-groups and,for p≥3,establishes a necessary and sufficient condition for inseparability.     

Semidirect sum of groups in which endomorphisms are generated by inner automorphisms

An I-E group is a group in which every endomorphism is finitely generated by its inner automorphisms. In this paper a characterization for a semidirect sum of I-E groups to be an I-E group is obtained and some well-known results are generalized. We then use this characterization to prove that a semidirect sum of finite I-E groups will again be an I-E group if the normal semidirect summand is unique and fully invariant. Conditions for a group to be an I-E group are also given.

     

G匚W上的泊松群胚结构

从泊松作用的角度考察了群胚上的半直积结构,定义了泊松群胚对泊松群胚的泊松作用,讨论了其性质,并证明了两个泊松群胚的半直积仍是泊松群胚,从而对群胚的半直积结构有了更多的认识.     

弱Clifford拟正则半群的半直积和圈积

本文给出两个么半群Ｓ和Ｔ的半直积和圈积为弱Ｃｌｉｆｆｏｒｄ拟正则么半群的充要条件和半直积的结构，同时还讨论了弱Ｃｌｉｆｆｏｒｄ拟正则么半群的最小群同余与半直积的最小群同余之间的关系．     

Semidirect imbedding problem with a metabelian kernel

In the paper one proves that in the case of a number field, for the solution of the semidirect imbedding problem with a metabelian kernel one can take a field.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Instituta im. V. A. Steklova AN SSSR, Vol. 100, pp. 81–85, 1980.     

On the question of embedding a semigroup into a semiband

In this paper we present a new embedding of a semigroups into a semiband (idempotent-generated semigroup) of depth 4 (every element is the product of 4 idempotents) using a semidirect product construction. Our embedding does not assume that S is a monoid (although it assumes a weaker condition) and works also for (non-monoid) regular semigroups. In fact, this semidirect product construction works particularly well if the semigroup is regular: we can choose the semiband to have depth 2. We shall see that many properties of S are preserved by this construction and we shall compare it to other known embeddings.     

Semidirect Products and Split Short Five Lemma in Normal Categories

In this paper we study a generalization of the notion of categorical semidirect product, as defined in [6], to a non-protomodular context of categories where internal actions are induced by points, like in any pointed variety. There we define semidirect products only for regular points, in the sense we explain below, provided the Split Short Five Lemma between such points holds, and we show that this is the case if the category is normal, as defined in [12]. Finally, we give an example of a category that is neither protomodular nor Mal’tsev where such generalized semidirect products exist.     

Some subgroups of the full linear group

Further observations are made on the author's earlier paper (Ref. Zh. Mat., 1977, 5A284) dealing with the lattice H of all subgroups of the full linear group GL(n, K) over a field K that contain the group K of diagonal matrices. It is noted, for example, that for an infinite field K all subgroups inD(n, K) are algebraic; a subgroup in H is connected if and only if it is a net subgroup; the lattice of all connected subgroups in H is isomorphic to the lattice of all marked topologies onn points; any subgroup H in H is a semidirect product H=A·H_o of a maximal connected normal subgroup H_o of H and a finite group A of, permutation matrices.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 71, pp. 42–46, 1977.     

LR-C半群的半直积

给出了两个半群的半直积是LR-C半群的充要条件.     

A Brief Note on the Noncoprime Regular Module Problem

Ukrainian Mathematical Journal - We consider a special configuration in which a finite group A acts by automorphisms on a finite group G and the semidirect product GA acts on the vector space V by...     

半环半直积的同构定理

半群半直积及封闭性刻划于文[1],为将半直积的研究推广至半环中,本文首先在交换半环与交换半群的直积上定义加法及乘法运算,从而构造了一类半环;半环半直积．并讨论了半环半直积的同构等问题．     

图的极大Tutte集的几个有效算法

图G=(V,E)的Tutte集定义为X■V(G)满足ω_o(G-X)一|X|=def(G).若不存在Tutte集Y■X,则称X为图G的极大Tutte集.通过找极大extreme集和D-图的极大独立集给出一般图G的找极大Tutte集的两个有效算法,并给出结论:X■V(G)是二部图G的极大Tutte集当且仅当X为二部图G的最小覆盖,从而得到找二部图G的极大Tutte集的一个有效算法.     

不相交斯泰纳和柯克曼三元系大集两定理(一)

给定一个斯泰纳或柯克曼三元系,介绍其大集的生成方法;得到其大集存在条件的判据是一个位差各异的循环数;柯克曼三元系其大集判据是,不能分解的柯克曼三元系有大集,能分解的无大集.     

Almost Factorizable Orthodox Semigroups

In this paper, we investigate idempotent separating and arbitrary homomorphic images of semidirect products of bands by groups. We give characterizations for idempotent separating homomorphic images of semidirect products, and show that the class of all idempotent separating homomorphic images is strictly contained in the class of all homomorphic images. Furthermore, we give a characterization of all homomorphic images.     

A bijection between the adjoint and coadjoint orbits of a semidirect product

We prove that there exists a geometric bijection between the sets of adjoint and coadjoint orbits of a semidirect product, provided a similar bijection holds for particular subgroups. We also show that under certain conditions the homotopy types of any two orbits in bijection with each other are the same. We apply our theory to the examples of the affine group and the Poincaré group, and discuss the limitations and extent of this result to other groups.     

The ABCs of Magnetic Monopole Dynamics

We revisit the explicit solution of Newton's equation of motion (mass times acceleration equals force) for a (pointlike, massive) magnetic monopole moving in the Coulomb field of a (fixed, pointlike) electric charge or, equivalently, of a (pointlike, massive) electric charge moving in the magnetic field of a (fixed) magnetic monopole.     

AUTOMORPHISM GROUPS OF 4-VALENT CONNECTED CAYLEY GRAPHS OF p-GROUPS

61. IntroductionLet G be a trite grouP and S a subs6t of G such thst 1' S and S = S--1. The Cayleygraph X = Cay(G, S) Of G with respect to S is defined to have vertex set V(X) = G and edgeset E(X) = {(g, ag) I g E G, s E' S}. ~ the defection the following two faCts are obvious:(1) the automorphism group Ant(X) of X contains GR, the right regular representation ofG, as a subgroup, and (2) X is cormected if and only if S generates the group G.FOr a Cayley graph X = Cay(G, S) Of …     

On a Class of Dubreil-Jacotin Semigroups

The aim of this paper is to study a class of strong Dubreil-Jacotin semigroups, so-called split integral Dubreil-Jacotin semigroups. We establish the structure of split integral Dubreil-Jacotin semigroups in terms of the cartesian ordered semidirect product of an ordered monoid and an ordered group. Also, the lexicographic ordered semidirect product is considered. These results extend main results in [1].