Groups with restrictions on subgroups of infinite rank.

DOI10.4171/RMI/792zbMath1322.20029OpenAlexW2086673580MaRDI QIDQ742884

Maria De Falco, Francesco de Giovanni, Carmela Musella, Nadir Trabelsi

Publication date: 19 September 2014

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/rmi/792

zbMATH Keywords

locally finite groupslocally graded groupscommutator subgroupsubgroups of infinite rank, Prüfer rank

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) General structure theorems for groups (20E34) Generalizations of solvable and nilpotent groups (20F19) Chains and lattices of subgroups, subnormal subgroups (20E15) Derived series, central series, and generalizations for groups (20F14) Local properties of groups (20E25)

Related Items (22)

GROUPS OF INFINITE RANK WITH A NORMALIZER CONDITION ON SUBGROUPS ⋮ On groups whose subgroups of infinite rank are Sylow permutable. ⋮ Groups whose subgroups of infinite rank are closed in the profinite topology ⋮ GROUPS OF INFINITE RANK WITH NORMALITY CONDITIONS ON SUBGROUPS WITH SMALL NORMAL CLOSURE ⋮ Groups with many abelian or self-normalizing subgroups ⋮ Groups whose proper subgroups of infinite rank have a transitive normality relation. ⋮ Groups whose proper subgroups are metahamiltonian-by-finite ⋮ Infinite minimal non-hypercyclic groups ⋮ Groups with some restrictions on non-Baer subgroups ⋮ Groups with an Engel restriction on proper subgroups of infinite rank ⋮ Large soluble groups and the control of embedding properties. ⋮ Infinite groups with rank restrictions on subgroups. ⋮ Groups with many subgroups having polycyclic-by-finite layers or derived subgroup ⋮ A note on groups of infinite rank with modular subgroup lattice. ⋮ Groups with Finitely Many Homomorphic Images of Finite Rank ⋮ A note on uncountable groups with modular subgroup lattice ⋮ Groups of infinite rank with a locally finite term in the lower central series. ⋮ Groups with many modular or self-normalizing subgroups ⋮ Unnamed Item ⋮ Groups Whose Proper Subgroups of Infinite Rank Have Polycyclic Conjugacy Classes ⋮ Groups whose proper subgroups of infinite rank are finite-by-hypercentral or hypercentral-by-finite ⋮ Groups of infinite rank with finite conjugacy classes of subnormal subgroups.

Cites Work

• Theorem on groups of finite special rank
• Groups Whose Finite Homomorphic Images are Metahamiltonian
• О Бесконечных Группах типа Миллера — Морено

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