Search results for "Àlgebra"
showing 5 items of 65 documents
On some classes of supersoluble groups
2007
[EN] Finite groups G for which for every subgroup H and for all primes q dividing the index |G:H| there exists a subgroup K of G such that H is contained in K and |K:H|=q are called Y-groups. Groups in which subnormal subgroups permute with all Sylow subgroups are called PST-groups. In this paper a local version of the Y-property leading to a local characterisation of Y-groups, from which the classical characterisation emerges, is introduced. The relationship between PST-groups and Y-groups is also analysed.
Finite groups with all minimal subgroups solitary
2016
We give a complete classification of the finite groups with a unique subgroup of order p for each prime p dividing its order. All the groups considered in this paper will be finite. One of the most fruitful lines in the research in abstract group theory during the last years has been the study of groups in which the members of a certain family of subgroups satisfy a certain subgroup embedding property. The family of the subgroups of prime order (also called minimal subgroups) has attracted the interest of many mathematicians. For example, a well-known result of Itˆo (see [8, Kapitel III, Satz 5.3; 9]) states that a group of odd order with all minimal subgroups in the center is nilpotent. Th…
Relations between {K, s + 1}-potent matrices and different classes of complex matrices
2013
In this paper, {K,s+1}-potent matrices are considered. A matrix A∈C^(n×n) is called {K,s+1}-potent when K A^(s+1) K = A where K is an involutory matrix and s∈{1,2,3,¿}. Specifically, {K,s+1}-potent matrices are analyzed considering their relations to different classes of complex matrices. These classes of matrices are: {s+1}-generalized projectors, {K}-Hermitian matrices, normal matrices, and matrices B∈C^(n×n) (anti-)commuting with K or such that KB is involutory, Hermitian or normal. In addition, some new relations for K-generalized centrosymmetric matrices have been derived.
Matrices A such that R A = A^{s + 1} R when R^k = I
2013
This paper examines matrices A∈C^(n×n) such that R A = A^(s+1) R where R^k = I, the identity matrix, and where s and k are nonnegative integers with k⩾2. Spectral theory is used to characterize these matrices. The cases s = 0 and s⩾1 are considered separately since they are analyzed by different techniques.
Eilenberg Theorems for Many-sorted Formations
2019
A theorem of Eilenberg establishes that there exists a bijectionbetween the set of all varieties of regular languages and the set of all vari-eties of finite monoids. In this article after defining, for a fixed set of sortsSand a fixedS-sorted signature Σ, the concepts of formation of congruenceswith respect to Σ and of formation of Σ-algebras, we prove that the alge-braic lattices of all Σ-congruence formations and of all Σ-algebra formationsare isomorphic, which is an Eilenberg's type theorem. Moreover, under asuitable condition on the free Σ-algebras and after defining the concepts offormation of congruences of finite index with respect to Σ, of formation offinite Σ-algebras, and of form…