The rank of the factor-group modulo the hypercenter and the rank of the some hypocenter of a group.

DOI10.2478/s11533-013-0284-yzbMath1316.20039OpenAlexW1985803223MaRDI QIDQ386367

Leonid A. Kurdachenko, Javier Otal

Publication date: 9 December 2013

Published in: Central European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s11533-013-0284-y

zbMATH Keywords

locally finite groupsSchur theoremlower central serieshypercentral groupsupper central seriesBaer theoremgeneralized radical groupsgroups of finite special rank

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Generalizations of solvable and nilpotent groups (20F19) Derived series, central series, and generalizations for groups (20F14) Local properties of groups (20E25)

Related Items (14)

The metanorm and its influence on the group structure ⋮ Unnamed Item ⋮ On some generalizations of Baer's theorem ⋮ On an analogue of a theorem of P. Hall for infinite dimensional linear groups ⋮ Unnamed Item ⋮ Bounds for the generalization of Baer's type theorems ⋮ On the relationships between central series in some locally finite groups ⋮ Groups whose factor group modulo the upper hypercenter is of finite 0-rank ⋮ Groups with Chernikov factor-group by hypercentral. ⋮ On the structure of some groups having finite contranormal subgroups ⋮ On the relationships between the factors of the upper and lower central series in some non-periodic groups ⋮ Unnamed Item ⋮ On groups whose factor-group modulo the hypercentre has finite section \(p\)-rank. ⋮ On the structure and some numerical properties of subgroups and factor-groups defined by automorphism groups

Cites Work

• Powerful \(p\)-groups. I: Finite groups.
• The Schur property and groups with uniform conjugacy classes
• Multiplicators and groups with finite central factor-groups
• Endlichkeitskriterien für Kommutatorgruppen
• Groups with boundedly finite classes of conjugate elements
• The ranks of central factor and commutator groups
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