Results 1 to 10 of about 1,920 (200)
Groups with minimax commutator subgroup [PDF]
International Journal of Group Theory, 2014 A result of Dixon, Evans and Smith shows that if $G$ is a locally (soluble-by-finite) group whose proper subgroups are (finite rank)-by-abelian, then $G$ itself has this property, i.e. the commutator subgroup of~$G$ has finite rank.
Francesco de Giovanni, Trombetti
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Groups whose Proper Subgroups of Infinite Rank are Minimax-by-Nilpotent or Nilpotent-by-Minimax [PDF]
Advances in Group Theory and Applications, 2020 Let M denote the class of of soluble-by-finite minimax groups, and N the class of nilpotent groups. The main result states that if G is a group of infinite rank whose proper subgroups of infinite rank are MN-groups, then G is either in MN or it is a ...
Amel Zitouni
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On groups with many normal subgroups [PDF]
International Journal of Group Theory, 2023 The structure of groups which are rich in normal subgroups has been investigated by several authors. Here, we prove that if a radical group G has normal deviation, which means that the set of its non-normal subgroups satisfies a very weak chain condition,
Alessio Russo, Mario Viscusi
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On invariant ideals in group rings of torsion-free minimax nilpotent groups
Researches in Mathematics, 2023 Let $k$ be a field and let $N$ be a nilpotent minimax torsion-free group acted by a solvable group of operators $G$ of finite rank. In the presented paper we study properties of some types of $G$-invariant ideals of the group ring $kN$.
A.V. Tushev
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Groups with soluble minimax conjugate classes of subgroups [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2008 A classical result of Neumann characterizes the groups in which each subgroup has finitely many conjugates only as central-by-finite groups. If X is a class of groups, a group G is said to have X-conjugate classes of subgroups if G/coreG(NG(H)) 2 X for ...
Francesco Russo
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Sequential Minimax Search for Multi-Layer Gene Grouping [PDF]
IEEE Access, 2019 Many areas of exploratory data analysis need to deal with high-dimensional data sets. Some real life data like human gene have an inherent structure of hierarchy, which embeds multi-layer feature groups.
Wenting Wang +3 more
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Minimax Group Fairness: Algorithms and Experiments [PDF]
Proceedings of the 2021 AAAI/ACM Conference on AI, Ethics, and Society, 2021 We consider a recently introduced framework in which fairness is measured by worst-case outcomes across groups, rather than by the more standard differences between group outcomes. In this framework we provide provably convergent oracle-efficient learning algorithms (or equivalently, reductions to non-fair learning) for minimax group fairness. Here the
Emily Diana +4 more
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On some commutative invariants of modules over minimax nilpotent groups
Доповiдi Нацiональної академiї наук України, 2022 In the paper we introduce a finite system of invariants for modules over minimax nilpotent groups which consists of classes of equivalent prime ideals of the group algebra of an Abelian minimax group. In particuly, introduced system of invariants allows
A.V. Tushev
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Groups with Finitely Many Isomorphism Classes of Non-Normal Subgroups [PDF]
Advances in Group Theory and Applications, 2020 We study groups in which the non-normal subgroups fall into finitely many isomorphism classes. We prove that a locally generalized radical group with this property is abelian-by-finite and minimax.
Leonid A. Kurdachenko +2 more
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On the structure of groups admitting faithful modules with certain conditions of primitivity
Researches in Mathematics, 2023 In the paper we study structure of soluble-by-finite groups of finite torsion-free rank which admit faithful modules with conditions of primitivity. In particular, we prove that under some additional conditions if an infinite finitely generated linear ...
A.V. Tushev
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