Groups whose proper subgroups of infinite rank have a transitive normality relation.

DOI10.1007/s00009-013-0321-xzbMath1311.20038OpenAlexW2051996128MaRDI QIDQ382081

Maria De Falco, Carmela Musella, Francesco de Giovanni

Publication date: 18 November 2013

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-013-0321-x

zbMATH Keywords

transitive normalityT-groupsalmost normal subgroupsgeneralized radical groupsnearly normal subgroupssubgroups of infinite rank

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) 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) FC-groups and their generalizations (20F24)

Related Items (11)

GROUPS OF INFINITE RANK WITH A NORMALIZER CONDITION ON SUBGROUPS ⋮ GROUPS OF INFINITE RANK WITH NORMALITY CONDITIONS ON SUBGROUPS WITH SMALL NORMAL CLOSURE ⋮ A note on groups whose proper subgroups are quasihamiltonian-by-finite ⋮ Infinite minimal non-hypercyclic groups ⋮ Uncountable groups with restrictions on subgroups of large cardinality. ⋮ A NOTE ON GROUPS WHOSE PROPER LARGE SUBGROUPS HAVE A TRANSITIVE NORMALITY RELATION ⋮ Large soluble groups and the control of embedding properties. ⋮ On locally graded minimal non-(finite-by-hypercentral) groups ⋮ Infinite groups with rank restrictions on subgroups. ⋮ Groups of infinite rank with a locally finite term in the lower central series. ⋮ Groups whose proper subgroups of infinite rank are finite-by-hypercentral or hypercentral-by-finite

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