On metahamiltonian groups of infinite rank.

DOI10.1016/j.jalgebra.2014.03.004zbMath1306.20037OpenAlexW2072539475MaRDI QIDQ402666

Maria De Falco, Carmela Musella, Francesco de Giovanni, Yaroslav P. Sysak

Publication date: 28 August 2014

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2014.03.004

zbMATH Keywords

groups of infinite rankgeneralized soluble groupsmetahamiltonian groups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generalizations of solvable and nilpotent groups (20F19) Chains and lattices of subgroups, subnormal subgroups (20E15) Local properties of groups (20E25)

Related Items (12)

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 whose proper subgroups of infinite rank have a transitive normality relation. ⋮ On a class of metahamiltonian groups. ⋮ Large soluble groups and the control of embedding properties. ⋮ Infinite groups with rank restrictions on subgroups. ⋮ A note on groups of infinite rank with modular subgroup lattice. ⋮ Groups with the weak minimal condition on non-normal non-abelian subgroups ⋮ Groups with some families of complemented subgroups ⋮ Groups of infinite rank with finite conjugacy classes of subnormal subgroups.

Cites Work

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• Groups with all subgroups permutable or of finite rank.
• Groups with all proper subgroups (finite rank)-by-nilpotent
• Locally (soluble-by-finite) groups with all proper non-nilpotent subgroups of finite rank
• Theorem on groups of finite special rank
• On Groups in Which Every Subgroup of Infinite Rank Is Subnormal of Bounded Defect
• On certain classes of infinite solvable groups
• GROUPS WHOSE PROPER SUBGROUPS OF INFINITE RANK HAVE FINITE CONJUGACY CLASSES

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