http://dspace.nbuv.gov.ua:80/handle/123456789/150336 2026-04-18T14:18:31Z http://dspace.nbuv.gov.ua:80/handle/123456789/156613 To the jubilee of Professor Yuriy Drozd This is a special issue of the journal devoted to the jubilee of the outstanding Ukrainian mathematician, one of the founder of our journal Professor Yuriy Drozd. 2005-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/156611 Wreath product of Lie algebras and Lie algebras associated with Sylow p-subgroups of finite symmetric groups Sushchansky, V.I.; Netreba, N.V. We define a wreath product of a Lie algebra L with the one-dimensional Lie algebra L1 over Fp and determine some properties of this wreath product. We prove that the Lie algebra associated with the Sylow p-subgroup of finite symmetric group Spm is isomorphic to the wreath product of m copies of L1. As a corollary we describe the Lie algebra associated with Sylow p-subgroup of any symmetric group in terms of wreath product of one-dimensional Lie algebras. 2005-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/156610 Abnormal subgroups and Carter subgroups in some infinite groups Kurdachenko, L.A.; Subbotin, I.Ya. t. 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. 2005-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/156609 Gorenstein matrices Dokuchaev, M.A.; Kirichenko, V.V.; Zelensky, A.V.; Zhuravlev, V.N. Let A = (aij ) be an integral matrix. We say that A is (0, 1, 2)-matrix if aij ∈ {0, 1, 2}. There exists the Gorenstein (0, 1, 2)-matrix for any permutation σ on the set {1, . . . , n} without fixed elements. For every positive integer n there exists the Gorenstein cyclic (0, 1, 2)-matrix An such that inx An = 2. If a Latin square Ln with a first row and first column (0, 1, . . . n − 1) is an exponent matrix, then n = 2m and Ln is the Cayley table of a direct product of m copies of the cyclic group of order 2. Conversely, the Cayley table Em of the elementary abelian group Gm = (2)×. . .×(2) of order 2 m is a Latin square and a Gorenstein symmetric matrix with first row (0, 1, . . . , 2 m − 1) and σ(Em) = 1 2 3 . . . 2 m − 1 2m 2 m 2 m − 1 2m − 2 . . . 2 1 . 2005-01-01T00:00:00Z