Infinite minimal non-hypercyclic groups

DOI10.1142/S0219498815501431zbMath1331.20044MaRDI QIDQ2949756

Marco Trombetti, Francesco de Giovanni

Publication date: 2 October 2015

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

zbMATH Keywords

locally graded groupslocally nilpotent groupssubgroups of infinite ranklocally supersoluble groupsminimal non-hypercentral groupsminimal non-hypercyclic groups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generalizations of solvable and nilpotent groups (20F19) Derived series, central series, and generalizations for groups (20F14) Local properties of groups (20E25)

Related Items (19)

Generalized nilpotency in uncountable groups ⋮ On minimal non-(residually nilpotent) locally graded groups ⋮ Unnamed Item ⋮ A note on groups whose proper subgroups are quasihamiltonian-by-finite ⋮ NILPOTENCY IN UNCOUNTABLE GROUPS ⋮ Groups with iterated restrictions on conjugacy classes ⋮ The pro-norm of a profinite group ⋮ Hall classes in linear groups ⋮ Finite skew braces of square-free order and supersolubility ⋮ Periodic linear groups factorized by mutually permutable subgroups ⋮ Large characteristic subgroups and abstract group classes ⋮ On locally graded minimal non-(finite-by-hypercentral) groups ⋮ Cohopfian groups and accessible group classes ⋮ Linear groups whose proper subgroups are close to being nilpotent ⋮ On groups with all proper subgroups finite-by-abelian-by-finite ⋮ Groups with all subgroups permutable or soluble of finite rank ⋮ Paranilpotency in uncountable groups ⋮ Unnamed Item ⋮ A constructive approach to accessible group classes

Cites Work

• Groups whose proper subgroups of infinite rank have a transitive normality relation.
• Groups with normality conditions for subgroups of infinite rank.
• Groups with restrictions on subgroups of infinite rank.
• Überauflösbare Gruppen
• On minimal non-supersoluble groups.
• Products of groups with finite rank
• Torsionsfreie Gruppen, deren Untergruppen alle subnormal sind. (Torsion free groups all of whose subgroups are subnormal)
• On the homology of hypercentral groups
• Triple factorization by locally supersoluble groups
• Minimal nicht überauflösbare, endliche Gruppen
• A group with trivial centre satisfying the normalizer condition
• Remarks on centrality and cyclicity in linear groups
• A note on groups of infinite rank whose proper subgroups are abelian-by-finite
• Remarks on the Upper Centralc Series of a Group
• Groups with few non-nilpotent subgroups
• On finite minimal non-nilpotent groups

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