1,721,004 research outputs found
On arrangement of subgroups in groups and related topics: some recent developments
No full textInvestigation of groups satisfying certain conditions, related to the subgroup arrangement, enabled algebraists to introduce and describe many important classes of groups. The roots of such investigations lie in the works by P. Hall, R. Carter, J. Rose, and Z. Borevich. Numerous interesting results in this area have been obtained lately by many authors. The main goal of this survey is to reflect some important new developments in study of subgroup arrangement in infinite groups
On arrangement of subgroups in groups and related topics: some recent developments
Get PDFInvestigation of groups satisfying certain conditions, related to the subgroup arrangement, enabled algebraists to introduce and describe many important classes of groups. The roots of such investigations lie in the works by P. Hall, R. Carter, J. Rose, and Z. Borevich. Numerous interesting results in this area have been obtained lately by many authors. The main goal of this survey is to reflect some important new developments in study of subgroup arrangement in infinite groups
Методи теорії груп для алгебр Лейбница: деякі помітні результати
No full textThe theory of Leibniz algebras has been developing quite intensively. Most of the results on the structural features of Leibniz algebras were obtained for finite-dimensional algebras and many of them over fields of characteristic zero. A number of these results are analogues of the corresponding theorems from the theory of Lie algebras. The specifics of Leibniz algebras, the features that distinguish them from Lie algebras, can be seen from the description of Leibniz algebras of small dimensions. However, this description concerns algebras over fields of characteristic zero. Some reminiscences of the theory of groups are immediately striking, precisely with its period when the theory of finite groups was already quite developed, and the theory of infinite groups only arose, i.e., with the time when the formation of the general theory of groups took place. Therefore, the idea of using this experience naturally arises. It is clear that we cannot talk about some kind of similarity of results; we can talk about approaches and problems, about application of group theory philosophy. Moreover, every theory has several natural problems that arise in the process of its development, and these problems quite often have analogues in other disciplines. In the current survey, we want to focus on such issues: our goal is to observe which parts of the picture involving a general structure of Leibniz algebras have already been drawn, and which parts of this picture should be developed further.Теорія алгебр Лейбніца розвивалася досить інтенсивно. Більшість результатів щодо структурних особливостей алгебр Лейбніца були отримані для скінченновимірних алгебр, і багато з них над полями нульової характеристики. Частина цих результатів є аналогами відповідних теорем з теорії алгебр Лі. Специфіку алгебр Лейбніца, особливості, що відрізняють їх від алгебр Лі, можна побачити з опису алгебр Лейбніца малих вимірностей. Однак цей опис стосується алгебр над полями нульової характеристики. Деякі спогади про теорію груп відразу кидаються в очі, а саме спогади, пов'язані з тим періодом, коли теорія скінченних груп була вже досить розвиненою, а теорія нескінченних груп лише виникла, тобто з тим часом, коли відбувалося становлення загальної теорії груп. Тому закономірно виникає ідея використання цього досвіду. Зрозуміло, що не можна говорити про якусь подібність результатів; ми можемо говорити про підходи та задачі, про застосування філософії теорії груп. Більше того, кожна теорія має низку природних проблем, які виникають у процесі її розвитку, і ці проблеми досить часто мають аналоги в інших дисциплінах. У даній оглядовій статті зосередимось на споспостереженні того, які частини малюнка із загальною структурою алгебр Лейбніца вже були намальовані, а які частини цієї картини слід розвивати далі
On arrangement of subgroups in groups and related topics: some recent developments
No full textInvestigation of groups satisfying certain conditions, related to the subgroup arrangement, enabled algebraists to introduce and describe many important classes of groups. The roots of such investigations lie in the works by P. Hall, R. Carter, J. Rose, and Z. Borevich. Numerous interesting results in this area have been obtained lately by many authors. The main goal of this survey is to reflect some important new developments in study of subgroup arrangement in infinite groups
Abnormal subgroups and Carter subgroups in some infinite groups
No full textt. Some properties of abnormal subgroups in generalized soluble groups are considered. In particular, the transitivity
of abnormality in metahypercentral groups is proven. Also it is
proven that a subgroup H of a radical group G is abnormal in G
if and only if every intermediate subgroup for H coincides with its
normalizer in G. This result extends on radical groups the wellknown criterion of abnormality for finite soluble groups due to D.
Taunt. For some infinite groups (not only periodic) the existence
of Carter subgroups and their conjugation have been also obtained
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Abnormal subgroups and Carter subgroups in some infinite groups
No full textt. Some properties of abnormal subgroups in generalized soluble groups are considered. In particular, the transitivity
of abnormality in metahypercentral groups is proven. Also it is
proven that a subgroup H of a radical group G is abnormal in G
if and only if every intermediate subgroup for H coincides with its
normalizer in G. This result extends on radical groups the wellknown criterion of abnormality for finite soluble groups due to D.
Taunt. For some infinite groups (not only periodic) the existence
of Carter subgroups and their conjugation have been also obtained
Groups with finiteness conditions on some subgroup systems: a contemporary stage
Get PDFThis paper gives a brief historical survey of results in which certain systems of subgroups of a group satisfy various finiteness conditions
Groups with finiteness conditions on some subgroup systems: a contemporary stage
No full textThis paper gives a brief historical survey of results in which certain systems of subgroups of a group satisfy various finiteness conditions
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