1,720,994 research outputs found
“Gruppi con sottogruppi non-normali risolubili”, comunicazione tenuta nell'ambito del Convegno “XIX Congresso U.M.I.”, Bologna 2011
No full text“On symplectic nil-algebras”, comunicazione tenuta nell'ambito del Convegno Internazionale “Groups and Topological Groups 2010”, Wien 2010
No full text
“p-Groups with few Conjugacy Classes of Normalizers”, comunicazione tenuta nell'ambito del Convegno Internazionale “Advances in Group Theory and Applications”, Porto Cesareo (LE) 2011
No full text“On symplectic nil-algebras”, comunicazione tenuta nell'ambito del Convegno Internazionale “Ischia Group Theory 2010”, Ischia (NA), 2010
No full textLocally Graded Quotients of Locally Graded Groups
No full textA group G is said to be locally graded if every nontrivial, finitely generated subgroup of G has a nontrivial finite image. Every group can occur as a quotient of a locally
graded group. It is shown that the largest subgroup and quotient closed interior of the class of locally graded groups is the class of groups in which every simple quotient
of every finitely generated subgroup is finite. This article investigates conditions under which a given quotient of a locally graded group is locally graded, and the result is
used to get more precise condition for a quotient of a linear group to be locally graded
ON GROUPS WITH ALL SUBGROUPS SUBNORMAL OR SOLUBLE OF BOUNDED DERIVED LENGTH
No full textIn this paper we deal with locally graded groups whose subgroups are either subnormal or soluble of bounded derived length, say d. In particular, we prove that every locally (soluble-by-finite) group with this property is either soluble or an extension of a soluble group of derived length at most d by a finite group, which fits between a minimal simple group and its automorphism group. We also classify all the finite non-abelian simple groups whose proper subgroups are metabelian.Scientific and Technological Research Council of Turkey (TUBITAK) BIDEB 2219 International Post Doctoral Research Fellowship; TUBITAKThe authors would like to thank Prof. Howard Smith for interesting discussions and useful suggestions. This study was carried out during the first author's visit to the University of Salerno and is supported by The Scientific and Technological Research Council of Turkey (TUBITAK) BIDEB 2219 International Post Doctoral Research Fellowship. The first author thanks TUBITAK for the support
On varieties of groups with a word whose values are Engel
No full textLet m, n be positive integers, v a multilinear commutator word and w=v^m. Denote by v(G) and w(G) the verbal subgroups of a group G corresponding to v and w, respectively. We prove that the class of all groups G in which the w-values are n-Engel and w(G) is locally nilpotent is a variety (Theorem A). Further, we show that in the case where m is a prime-power the class of all groups G in which the w-values are n-Engel and v(G) has an ascending normal series whose quotients are either locally soluble or locally finite is a variety (Theorem B). We examine the question whether the latter result remains valid with m allowed to be an arbitrary positive integer. In this direction, we show that if m, n are positive integers, u a multilinear commutator word and v the product of 896 u-words, then the class of all groups G in which the v^m-values are n-Engel and the verbal subgroup u(G) has an ascending normal series whose quotients are either locally soluble or locally finite is a variety (Theorem C)
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