Перегляд за автором "Kurdachenko, L.A."

Сортувати за: Порядок: Результатів:

  • On the anticommutativity in Leibniz algebras 
    Kurdachenko, L.A.; Semko, N.N.; Subbotin, I.Ya. (Algebra and Discrete Mathematics, 2018)
    Lie algebras are exactly the anticommutative Leibniz algebras. In this article, we conduct a brief analysis of the approach to Leibniz algebras which based on the concept of the anti-center (Lie-center) and antinilpotency ...
  • On the contribution of D.I. Zaitsev to the Theory of Infinite Groups 
    Kirichenko, V.V.; Kurdachenko, L.A.; Otal, J.; Subbotin, I.Ya. (Algebra and Discrete Mathematics, 2012)
    We survey the most outstanding contributions due to D.I. Zaitsev in the Theory of Infinite Groups.
  • On the derivations of Leibniz algebras of low dimension 
    Kurdachenko, L.A.; Semko, M.M.; Yashchuk, V.S. (Доповіді НАН України, 2023)
    Let L be an algebra over a field F. Then L is called a left Leibniz algebra if its multiplication operations [⋅, ⋅] additionally satisfy the so-called left Leibniz identity: [[a,b],c] = [a,[b,c]] – [b,[a,c]] for all ...
  • On the existence of complements in a group to some abelian normal subgroups 
    Dixon, M.R.; Kurdachenko, L.A.; Javier Otal (Algebra and Discrete Mathematics, 2010)
    A complement to a proper normal subgroup H of a group G is a subgroup K such that G=HK and H∩K=⟨1⟩. Equivalently it is said that G splits over H. In this paper we develop a theory that we call hierarchy of centralizers to ...
  • On the influence of ideals and self-idealizing subalgebras on the structure of Leibniz algebras 
    Kurdachenko, L.A.; Pypka, A.A.; Subbotin, I.Ya. (Доповіді НАН України, 2021)
    The subalgebra A of a Leibniz algebra L is self-idealizing in L, if A = IL (A). In this paper we study the structure of Leibniz algebras, whose subalgebras are either ideals or self-idealizing. More precisely, we obtain ...
  • On the non–periodic groups, whose subgroups of infinite special rank are transitively normal 
    Kurdachenko, L.A.; Subbotin, I.Ya.; Velychko, T.V. (Algebra and Discrete Mathematics, 2020)
    This paper devoted to the non-periodic locally generalized radical groups, whose subgroups of infinite special rank are transitively normal. We proved that if such a group G includes an ascendant locally nilpotent subgroup ...
  • On the nonperiodic groups, whose subgroups of infinite special rank are transitively normal 
    Kurdachenko, L.A.; Subbotin, I.Ya.; Velychko, T.V. (Доповіді НАН України, 2020)
    This paper devoted to the nonperiodic locally generalized radical groups, whose subgroups of infinite special rank are transitively normal. We proved that if such a group G includes an ascendant locally nilpotent subgroup ...
  • On the role played by anticommutativity in Leibniz algebras 
    Kurdachenko, L.A.; Semko, N.N.; Subbotin, I.Ya. (Доповіді НАН України, 2019)
    Lie algebras are exactly the anticommutative Leibniz algebras. We conduct a brief analysis of the approach to Leibniz algebras which is based on the concept of anticenter (Lie-center) and antinilpotency (Lie nilpotentency).
  • On the structure of groups, whose subgroups are either normal or core-free 
    Kurdachenko, L.A.; Pypka, A.A.; Subbotin, I.Ya. (Доповіді НАН України, 2019)
    We investigate the influence of some natural types of subgroups on the structure of groups. A subgroup H of the group G is called core-free if CoreG(H) = 〈1〉. We study the groups, in which every subgroup is either normal ...
  • On the structure of Leibniz algebras whose subalgebras are ideals or core-free 
    Chupordia, V.A.; Kurdachenko, L.A.; Semko, N.N. (Algebra and Discrete Mathematics, 2020)
    An algebra L over a field F is said to be a Leibniz algebra (more precisely, a left Leibniz algebra) if it satisfies the Leibniz identity: [[a, b], c] = [a, [b, c]]−[b, [a, c]] for all a, b, c ∊ L. Leibniz algebras are ...
  • On the structure of Leidniz algebras, whose subalgebras are ideals or core-free 
    Chupordia, V.A.; Kurdachenko, L.A.; Semko, N.N. (Доповіді НАН України, 2020)
    An algebra L over a field F is said to be a Leibniz algebra (more precisely, a left Leibniz algebra), if it satisfies the Leibniz identity: [[a, b], c] = [a, [b, c]] — [b, [a, c]] for all a, b, c ∈ L. Leibniz algebras are ...
  • On the structure of some groups having finite contranormal subgroups 
    Kurdachenko, L.A.; Semko, N.N. (Algebra and Discrete Mathematics, 2021)
    Following J.S. Rose, a subgroup H of the group G is said to be contranormal in G, if G = Hᴳ. In a certain sense, contranormal subgroups are antipodes to subnormal subgroups. We study the structure of Abelian-by-nilpotent ...
  • On the structure of the algebra of derivations of cyclic Leibniz algebras 
    Kurdachenko, L.A.; Semko, M.M.; Yashchuk, V.S. (Algebra and Discrete Mathematics, 2021)
    We describe the algebra of derivation of finitedimensional cyclic Leibniz algebra.
  • On various rank conditions in infinite groups 
    Dixon, M.R.; Kurdachenko, L.A.; Subbotin, I.Ya. (Algebra and Discrete Mathematics, 2007)
    In the current survey the authors consider some ofthe main theorems concerning groups satisfying certain rank con-ditions. They present these theorems starting with recently estab-lished results. This order of exposition ...
  • S. N. Chernikov and the development of infinite group theory 
    Dixon, M.R.; Kirichenko, V.V.; Kurdachenko, L.A.; Otal, J.; Semko, N.N.; Shemetkov, L.A.; Subbotin, I.Ya. (Algebra and Discrete Mathematics, 2012)
    In this survey, the authors want to show the development and continuation of some studies, in which S.N.Chernikov stood as the main originator and to demonstrate clearly the extent of influence exerted by the ideas and ...
  • Some aspects of Leibniz algebra theory 
    Kirichenko, V.V.; Kurdachenko, L.A.; Pypka, A.A.; Subbotin, I.Ya. (Algebra and Discrete Mathematics, 2017)
    One of the key tendencies in the development of Leibniz algebra theory is the search for analogues of the basic results of Lie algebra theory. In this survey, we consider the reverse situation. Here the main attention is ...
  • Some related to pronormality subgroup families and the properties of a group 
    Kirichenko, V.V.; Kurdachenko, L.A.; Subbotin, I.Ya. (Algebra and Discrete Mathematics, 2011)
    Some influential families of subgroups such as pronormal subgroups, contranormal subgroups, and abnormal subgroups, their generalizations, characterizations, interplays between them and the group, and their connections to ...
  • The description of the automorphism groups of finitedimensional cyclic Leibniz algebras 
    Kurdachenko, L.A.; Pypka, O.O.; Subbotin, I.Ya. (Доповіді НАН України, 2022)
    In the study of Leibniz algebras, the information about their automorphisms (as well as about endomorphisms, derivations, etc.) is very useful. We describe the automorphism groups of finite-dimensional cyclic Leibniz ...
  • The groups whose cyclic subgroups are either ascendant or almost self-normalizing 
    Kurdachenko, L.A.; Pypka, A.A.; Semko, N.N. (Algebra and Discrete Mathematics, 2016)
    The main result of this paper shows a description of locally finite groups, whose cyclic subgroups are either almost self-normalizing or ascendant. Also, we obtained some natural corollaries of the above situation.