The ranks of central factor and commutator groups

DOI10.1017/S0305004112000412zbMath1272.20032arXiv1204.4641OpenAlexW3098797007MaRDI QIDQ4902498

Leonid A. Kurdachenko, P. V. Shumyatskij

Publication date: 15 January 2013

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.4641

zbMATH Keywords

finitely generated subgroupslocally finite groupslocally nilpotent groupsgroups of finite rankPrüfer ranklocally generalized radical groupsascending invariant series

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) General structure theorems for groups (20E34) Generalizations of solvable and nilpotent groups (20F19) Chains and lattices of subgroups, subnormal subgroups (20E15) FC-groups and their generalizations (20F24)

Related Items (17)

ON THE RANK OF A VERBAL SUBGROUP OF A FINITE GROUP ⋮ Nilpotent residual of fixed points ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Coprime automorphisms of finite groups ⋮ The rank of the factor-group modulo the hypercenter and the rank of the some hypocenter of a group. ⋮ Bounds for the generalization of Baer's type theorems ⋮ Extension of a Schur theorem to groups with a central factor with a bounded section rank. ⋮ On the relationships between central series in some locally finite groups ⋮ On countable coverings of word values in profinite groups. ⋮ Groups whose factor group modulo the upper hypercenter is of finite 0-rank ⋮ Engel sinks of fixed points in finite groups ⋮ Groups with many subgroups having polycyclic-by-finite layers or derived subgroup ⋮ On the relationships between the factors of the upper and lower central series in some non-periodic groups ⋮ Unnamed Item ⋮ On some properties of the upper central series in Leibniz algebras ⋮ On groups whose factor-group modulo the hypercentre has finite section \(p\)-rank.

Cites Work

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• Characterization of \(p\)-adic analytic groups in terms of wreath products
• The Schur property and groups with uniform conjugacy classes
• On some ranks of infinite groups.
• Beweis eines Satzes über diskrete Gruppen
• ON SOME TORSION-FREE GROUPS
• SOLUTION OF THE RESTRICTED BURNSIDE PROBLEM FOR GROUPS OF ODD EXPONENT
• The exponents of central factor and commutator groups

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