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Algebra and Discrete Mathematics, 2006, Issue 4, Pages 57–66 (Mi adm279)  

RESEARCH ARTICLE

On groups with the minimal condition for non-invariant decomposable abelian subgroups

F. N. Lyman, M. G. Drushlyak
Abstract: The infinite groups, in which there is no any infinite descending chain of non-invariant decomposable abelian subgroups ($md$-groups) are studied. Infinite groups with the minimal condition for non-invariant abelian subgroups, infinite groups with the condition of normality for all decomposable abelian subgroups and others belong to the class of $md$-groups. The complete description of infinite locally finite and locally soluble non-periodic $md$-groups is given, the connection of the class of $md$-groups with other classes of groups are investigated.
Keywords: group, subgroup, order of the group, involution, locally finite group, non-periodic group, decomposable abelian subgroup, minimal condition, condition of normality.
Received: 11.08.2006
Revised: 29.03.2006
Bibliographic databases:
Document Type: Article
Language: English
Citation: F. N. Lyman, M. G. Drushlyak, “On groups with the minimal condition for non-invariant decomposable abelian subgroups”, Algebra Discrete Math., 2006, no. 4, 57–66
Citation in format AMSBIB
\Bibitem{LymDru06}
\by F.~N.~Lyman, M.~G.~Drushlyak
\paper On groups with the minimal condition for non-invariant decomposable abelian subgroups
\jour Algebra Discrete Math.
\yr 2006
\issue 4
\pages 57--66
\mathnet{http://mi.mathnet.ru/adm279}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2319408}
\zmath{https://zbmath.org/?q=an:1116.20024}
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