Omega subgroups of pro-\(p\) groups.

DOI10.1007/s11856-008-1036-8zbMath1153.20028OpenAlexW2162479060MaRDI QIDQ948894

Jon González-Sánchez, Gustavo A. Fernández-Alcober, Andrei Jaikin-Zapirain

Publication date: 16 October 2008

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

Full work available at URL: https://doi.org/10.1007/s11856-008-1036-8

zbMATH Keywords

exponentspower subgroupspro-\(p\)-groupscentral seriespotent filtrationsomega subgroupspower-commutator conditions

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Derived series, central series, and generalizations for groups (20F14) Commutator calculus (20F12) Limits, profinite groups (20E18)

Related Items (27)

On pro-\(p\) groups with potent filtrations. ⋮ A \(p\)-nilpotency criterion. ⋮ Analytic pro-p groups of small dimensions ⋮ Advances on a construction related to the non-abelian tensor square of a group ⋮ Non-abelian tensor square and related constructions of \(p\)-groups ⋮ A BOUND ON THE p-LENGTH OF P-SOLVABLE GROUPS ⋮ Bounds for the exponent of the Schur multiplier ⋮ A bound for the exponent of the Schur multiplier of a finite \(p\)-group. ⋮ On weak commutativity in \(p\)-groups ⋮ The exponent of the non‐abelian tensor square and related constructions ofp‐groups ⋮ Commutators, centralizers, and strong conciseness in profinite groups ⋮ On bounded conciseness of words in residually finite groups ⋮ A characterization of powerful \(p\)-groups. ⋮ On bounded conciseness of Engel-like words in residually finite groups ⋮ On finiteness of some verbal subgroups in profinite groups ⋮ Positive laws on word values in residually-\(p\) groups. ⋮ Cohomology of finite \(p\)-groups of fixed nilpotency class ⋮ Finite \(p\)-central groups of height \(k\). ⋮ On \(w\)-maximal groups. ⋮ The \(q\)-tensor square of a powerful \(p\)-group ⋮ On finiteness of verbal subgroups ⋮ Kirillov's Orbit Method forp-Groups and Pro-pGroups ⋮ On finite \(p\)-groups satisfying given laws ⋮ Bounding the index of the agemo in finite \(p\)-groups. ⋮ On rational and concise words. ⋮ Cohomology of uniserial 𝑝-adic space groups ⋮ On conciseness of words in profinite groups.

Cites Work

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• The power structure of \(p\)-groups. I
• Torsion elements in \(p\)-adic analytic pro-\(p\) groups.
• On the structure of normal subgroups of potent \(p\)-groups.
• On \(p\)-saturable groups.
• \(p\)-adic analytic groups
• The power-commutator structure of finite p-groups
• The power structure of finite p-groups satisfying conditions like those of Lazard
• A Contribution to the Theory of Groups of Prime-Power Order
• Endliche Gruppen I

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