Weak Maximality Condition and Polycyclic Groups

DOI10.2307/2160789zbMath0829.20051OpenAlexW4239317019MaRDI QIDQ4327643

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Publication date: 10 April 1995

Full work available at URL: https://doi.org/10.2307/2160789

zbMATH Keywords

finitely generated subgroupspolycyclic groupspolycyclic-by-finite groupfinitely generated strongly restrained locally graded groupsstrongly restrained groups

Mathematics Subject Classification ID

Solvable groups, supersolvable groups (20F16) Generators, relations, and presentations of groups (20F05) Generalizations of solvable and nilpotent groups (20F19) Chains and lattices of subgroups, subnormal subgroups (20E15) Residual properties and generalizations; residually finite groups (20E26) Local properties of groups (20E25)

Related Items (18)

Groups in which the derived groups of all 2-generator subgroups are cyclic. ⋮ Generalized nilpotency in uncountable groups ⋮ On some classes of orderable groups ⋮ The local nilpotence theorem for 4-Engel groups revisited ⋮ A NILPOTENCY-LIKE CONDITION FOR INFINITE GROUPS ⋮ Locally finite groups with all subgroups normal-by-(finite rank) ⋮ Groups with an Engel restriction on proper subgroups of infinite rank ⋮ Which words spell ``almost nilpotent? ⋮ What do the Engel laws and positive laws have in common? ⋮ On laws of the form \(ab\equiv ba\) equivalent to the abelian law ⋮ A question of Paul Erdös and nilpotent-by-finite groups ⋮ Groups with no Free Subsemigroups ⋮ Locally graded groups with a condition on infinite subsets ⋮ Group Laws Implying Virtual Nilpotence ⋮ Milnor's alternative for finitely generated relatively free groups that are locally graded ⋮ Groups preserving the cardinality of subsets product under permutations ⋮ On centrally orderable groups ⋮ Some Engel conditions on infinite subsets of certain groups

Cites Work

• Unnamed Item
• Right-ordered groups
• Combinatorial conditions in residually finite groups. I
• Free subgroups in linear groups
• Two-Generator conditions for Residually Finite Groups

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