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

• Дата: 2018
• Автори: Lyman, F. N., Drushlyak, M. G.
• Формат: Стаття
• Мова: English
• Опубліковано: Lugansk National Taras Shevchenko University 2018
• Теми: group; subgroup; order of the group; involution; locally finite group; non-periodic group; decomposable abelian subgroup; minimal condition; condition of normality
• Онлайн доступ: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/906
• Назва журналу: Algebra and Discrete Mathematics

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.