Finite two-are transitive graphs admitting a ree simple group

ABSTRACT

The article is dedicated to some generalizations of minimax soluble groups satisfying common criterion of nilpotency, such that normality of maximal subgroups, nilpotency of the factor-group by the Frattini subgroup, normality of pronormal subgroups, non-existence of proper abnormal subgroups and so on.     

On sse-embedded subgroups of finite groups

Abstract

In this paper, we introduce the concept of sse-embedded subgroups of finite groups and present some new characterizations of solubility of finite groups using the sse-embedding property of subgroups. Furthermore, we discuss the sse-embedded subgroups in finite nonabelian simple groups. Some previously known results are generalized and unified.     

THE JOIN OF DISJOINT PERMUTABLE SUBGROUPS

ABSTRACT

The authors obtain a bound for the derived length of a finite group, which is the join of two disjoint permutable nilpotent subgroups, in terms of the derived lengths of the two subgroups.     

Abnormal,Pronormal, Contranormal,and Carter Subgroups in Some Generalized Minimax Groups

ABSTRACT

Some properties of abnormal and pronormal subgroups in generalized minimax groups are considered. For generalized minimax groups (not only periodic) whose locally nilpotent residual is nilpotent and satisfies Min-G the existence of Carter subgroups and their conjugations have been proven. Some generalizations of results of J. Rose on abnormal and contranormal subgroups have been also obtained.     

Free Subgroups in the Units of ℤ[K 8 × C p ]

Abstract

Marciniak and Sehgal (Marciniak, Z., Sehgal, S. K. (1997). Constructing free subgroups of integral group rings units. Proc. Amer. Math. Soc.125(4):1005–1009) constructed free subgroups in U(?[G]) whenever Ghas a non normal finite subgroup. In this paper we construct free subgroups in U(?[G]), where Gis a group whose subgroups are all normal.     

SUBGROUPS OF THE FREE SEMIGROUP ON A BIORDERED SET IN WHICH PRINCIPAL IDEALS ARE SINGLETONS

ABSTRACT

Easdown has conjectured that the subgroups of the free semigroup on an arbitrary biordered set are free. In this note a weaker conjecture is verified. It is shown that the subgroups of the free semigroup on a biordered set in which principal ideals are singletons are free. In addition, an expression is given for the ranks of the maximal subgroups. This generalizes a result due to Pastijn which involves the free semigroup on a rectangular biset.     

Cyclic conjugacy separability and conjugacy separability of certain HNN extensions

Abstract

In this note, we give a criterion for certain HNN extensions of cyclic conjugacy separable (respectively conjugacy separable) groups with infinite cyclic associated subgroups to be again cyclic conjugacy separable (respectively conjugacy separable).

Communicated by Alexander Olshanskii     

Zur Klassifikation differenzierbarer Gruppen

We want to classify differentiable groups in terms of Lie groups and formal groups. This note contains a first essential step in this direction: Differentiable groups can always be embedded as dense subgroups of locally compact groups.

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Herrn W. Thimm zum 60. Geburtstag gewidmet     

Defining Relations for the Carpet Subgroups of Chevalley Groups over Fields

The carpet subgroups admitting a Bruhat decomposition and different from Chevalley groups are exhausted by the groups lying between the Chevalley groups of type \( B_{l} \), \( C_{l} \), \( F_{4} \), or \( G_{2} \) over various imperfect fields of exceptional characteristic 2 or 3, the larger of which is an algebraic extension of the smaller field. Moreover, as regards the types \( B_{l} \) and \( C_{l} \), these subgroups are parametrized by the pairs of additive subgroups one of which may fail to be a field and, for the type \( B_{2} \), even both additive subgroups may fail to be fields. In this paper for the carpet subgroups admitting a Bruhat decomposition we present the relations similar to those well known for Chevalley groups over fields.

     

Finite groups with abelian second maximal subgroups

Abstract

In this article, we give a complete classification of finite groups whose second maximal subgroups are all abelian.     

Generalised linear model trees with global additive effects

Model-based trees are used to find subgroups in data which differ with respect to model parameters. In some applications it is natural to keep some parameters fixed globally for all observations while asking if and how other parameters vary across subgroups. Existing implementations of model-based trees can only deal with the scenario where all parameters depend on the subgroups. We propose partially additive linear model trees (PALM trees) as an extension of (generalised) linear model trees (LM and GLM trees, respectively), in which the model parameters are specified a priori to be estimated either globally from all observations or locally from the observations within the subgroups determined by the tree. Simulations show that the method has high power for detecting subgroups in the presence of global effects and reliably recovers the true parameters. Furthermore, treatment–subgroup differences are detected in an empirical application of the method to data from a mathematics exam: the PALM tree is able to detect a small subgroup of students that had a disadvantage in an exam with two versions while adjusting for overall ability effects.

     

On the behavior of π-submaximal subgroups under homomorphisms

Abstract

We construct examples that show the difference in behavior of π-maximal and π-submaximal subgroups under group homomorphisms.     

Pairwise -connected Products of Certain Classes of Finite Groups

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.     

The norm theorem for quadratic forms over a field of characteristic 2

ABSTRACT

In this paper we prove that a finite group G is isomorphic to the finite simple group L _n (q) with n ≥ 3 if and only if they have the same set of order of solvable subgroups.

     

On the 2-Categories of Weak Distributive Laws

ABSTRACT

Let G be a torsion-free group with all subgroups subnormal of defect at most 4. We show that G is nilpotent of class at most 4.     

The Existence of p-Blocks with a Submaximal-Subgroup of a Sylow p-Subgroup as Defect Group

Abstract

In this paper,we will determine the existence of blocks with submaximal subgroups of Sylow p-subgroups of a finite group G as defect groups.     

Sottogruppi normali er-omomorfismi completi tra gruppi

Summary The behavior of normal subgroups under complete lattice homomorphisms between groups is investigated. Known results in this context for lattice isomorphisms are shown to be still valid, with minor changes, in this more general setting.

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L'A. ringrazia il C.N.R. e il Seminario Matematico dell'Università di Kiel per un supporto finanziario e per l'ospitalità ivi goduta durante la stesura di gran parte del presente lavoro.     

Die Normalteiler symplektischer Gruppen¶über Bewertungsringen mit einer¶Restklassenkörper-Charakteristik ≠ 2

In the present paper the normal subgroups of a symplectic group SP(L of a lattice L (not necessarily modular) over a valuation ring, whose residue class field has not characteristic 2, are characterised by an interval condition and the occuring intervals are described by the corresponding factor group given by the interval ends. This generalizes results of C. Riehm [7].

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Received: 8 September 1998     

A Generalized Hughes Property of Finite Groups

Abstract

A Hughes cover for exponent p(pa prime number) of a finite group is a union of subgroups whose (non-empty) complement consists of elements of order p. A proper Hughes subgroup is an instance of a Hughes cover; and its parent group is soluble by a well-known result of Hughes and Thompson. More generally an earlier result of the authors shows that a group with a Hughes cover of fewer than psubgroups is soluble. This article treats the insoluble groups having a Hughes cover for exponent pwith exactly psubgroups: the almost simple groups with this property form a restricted class of projective special linear groups.