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For the field F and F-vector space A, let G be a subgroup of GL(F, A), the group of invertible F-linear transformations of A. A subspace B of A is G-core-free if ∩g∈GgB=0. In this article, we discu...

Let A be a vector space over a field F and let G be a subgroup of $$\mathrm{GL}(F,A)$$. This paper gives some further linear variations of a well-known theorem due to Philip Hall. For example we prove that if F has characteristic p and B is a finite dimensional subspace of A of dimension d such that A / B is G-hypercentral, and if G has finite section p-rank r, then the upper G-hypercenter has finite codimension in A, bounded by a function of d, r only. Analogues of these results in characteristic 0 are also obtained.

A subgroup of a group is contranormal if its normal closure coincides with the group. We call such groups without proper contranormal subgroups contranormal-free. In this paper we prove various results concerning contranormal-free groups proving, for example that locally generalized radical contranormal-free groups which have finite section rank are hypercentral.

We study the endomorphisms and derivations of an infinite-dimensional cyclic Leibniz algebra. Among others it was found that if [Formula: see text] is a cyclic infinite-dimensional Leibniz algebra over a field [Formula: see text], then the group of all automorphisms of [Formula: see text] is isomorphic to a multiplicative group of the field [Formula: see text]. The description of an algebra of derivations of a cyclic infinite-dimensional Leibniz algebra has been obtained.

For the field [math] and [math] -vector space [math] , let [math] be a subgroup of [math] , the group of invertible [math] -linear transformations of [math] . A subspace [math] of [math] is [math] -contrainvariant if [math] . We discuss groups [math] and vector spaces [math] such that every subspace of [math] is either [math] -invariant or [math] -contrainvariant.

The authors prove that if G is a group such that G/ζ∞(G) has finite 0-rank r and if every periodic factor group of G is locally finite, then G contains a normal subgroup K of finite 0-rank ...

In this paper we obtain the description of the Leibniz algebras whose subalgebras are ideals.

The Generalized Rectangular Fuzzy Assessment Model (GRFAM) is applied for the evaluation of student group acquisition of the van Hiele levels of geometric reasoning and an example is presented illustrating our results. The GRFAM is a variation of the Center of Gravity defuzzification technique created in an effort to treat better the ambiguous assessment cases being at the boundaries between any two successive assessment grades.

We study groups in which the non-abelian subgroups fall into finitely many isomorphic classes. We prove that a locally generalized radical group with this property is abelian-by-finite and reduced minimax. The same conclusion holds for locally generalized coradical groups. Here a generalized radical group is a group with an ascending series whose factors are either locally nilpotent or locally finite, and a generalized coradical group is a group with a descending series whose factors are either locally nilpotent or locally finite.

We apply the Triangular Fuzzy Assessment Model (TFAM) for analogical reasoning skills assessment. The TFAM is a new original model based on the Centre of Gravity (COG) defuzzification technique, which we have properly adapted and used in earlier papers as an assessment method of several human activities. The main idea of the TFAM is the replacement of the rectangles appearing in the graph of the COG technique by isosceles triangles sharing common parts. In this way, we can treat better the ambiguous cases of scores being at the boundaries between two successive linguistic characterizations (grades) of the level of the individuals’ performance. An application is also presented illustrating our results in practice, where the TFAM is compared with two traditional assessment methods (calculation of the means and of the GPA index) based on principles of the bivalent logic (yes-no).

Fuzzy logic due to its nature of characterizing each case with multiple values offers is a rich field of resources covering the assessment of situations characterized by a degree of fuzziness and/or uncertainty. In this paper, we present two different fuzzy assessment models: The Centre of Gravity (COG) model and Trapezoidal Fuzzy Assessment Model (TRFAM). The last one is a new model covering the ambiguous cases being at the boundaries between two successive assessment intervals. An application (students' assessment) is also presented, through which the above methods are compared to each other and also with two traditional assessment methods based on principles of bivalent logic (the calculation of means and of the GPA index). Some useful conclusions are drawn about the characteristics of the above fuzzy assessment models.

Let R be a ring and G a group. An R-module A is said to be minimax if A includes an noetherian submodule B such that A=B is artinian. The authors study a ZG-module A such that A/C_A(H) is minimax (as a Z-module) for every proper not finitely generated subgroup H., arXiv admin note: text overlap with arXiv:1302.2115

A subalgebra [Formula: see text] of a Leibniz algebra [Formula: see text] is called a contraideal, if an ideal, generated by [Formula: see text] coincides with [Formula: see text]. We study the Leibniz algebras, whose subalgebras are either ideal or contraideal.

We established several new criteria for existence of complements and supplements to some normal abelian subgroups in groups. In passing, as one of the many useful applications and corollaries of these results, we obtained a description of some finitely generated soluble groups of finite Hirsch–Zaitsev rank. As another application of our results, we obtained a D.J.S. Robinson's theorem on structure of finitely generated soluble groups of finite section rank. The original proof of this theorem was homological, but all proofs in this paper, including this one, are purely group-theoretical.

In this paper, we obtain the description of hyperabelian Leibniz algebras, whose subideals are ideals.

New results on tight connections among pronormal, abnormal and contranormal subgroups of a group have been established. In particular, new characteristics of pronormal and abnormal subgroups have been obtained.