On some ranks of infinite groups.

DOI10.1007/S11587-007-0004-7zbMath1142.20016OpenAlexW2027877209MaRDI QIDQ2467938

Martyn R. Dixon, Nikolay V. Polyakov, Leonid A. Kurdachenko

Publication date: 29 January 2008

Published in: Ricerche di Matematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11587-007-0004-7

zbMATH Keywords

\(p\)-ranksascending seriesgroups of bounded ranktorsion-free ranksHirsch-Zaicev rankslocally generalized radical groups

Mathematics Subject Classification ID

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 (15)

SOME CRITERIA FOR EXISTENCE OF SUPPLEMENTS TO NORMAL SUBGROUPS AND THEIR APPLICATIONS ⋮ GROUPS IN WHICH THE NORMAL CLOSURES OF CYCLIC SUBGROUPS HAVE FINITE SECTION RANK ⋮ Groups with finitely many isomorphic classes of non-abelian subgroups ⋮ Unnamed Item ⋮ A note on skew linear groups of finite rank ⋮ Unnamed Item ⋮ Groups with the weak maximal condition on non-permutable subgroups ⋮ On the structure of some infinite dimensional linear groups ⋮ Locally soluble infinite-dimensional linear groups with restrictions on nonAbelian subgroups of infinite ranks ⋮ Groups whose factor group modulo the upper hypercenter is of finite 0-rank ⋮ The ranks of central factor and commutator groups ⋮ On the structure of some Noetherian modules over group rings ⋮ On the relationships between the factors of the upper and lower central series in some non-periodic groups ⋮ Groups in which the normal closures of cyclic subgroups have bounded finite Hirsch-Zaitsev rank ⋮ On groups whose factor-group modulo the hypercentre has finite section \(p\)-rank.

Cites Work

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• Radical groups of finite Abelian subgroup rank
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• Embedding groups in locally (soluble-by-finite) simple groups
• Residual Properties of Some Classes of Infinite Soluble Groups
• On Infinite Soluble Groups-I
• Soluble products of nilpotent groups

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