A 2-generated just-infinite profinite group which is not positively generated.

DOI10.1007/BF02772214zbMath1074.20024OpenAlexW2039700504MaRDI QIDQ1885651

Andrea Lucchini

Publication date: 11 November 2004

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

Full work available at URL: https://doi.org/10.1007/bf02772214

zbMATH Keywords

finitely generated profinite groupsrandom elementsepimorphic imagespositively generated profinite groups

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Automorphisms of infinite groups (20E36) Limits, profinite groups (20E18) Probabilistic methods in group theory (20P05)

Related Items (7)

Random generation of finite and profinite groups and group enumeration. ⋮ A finitely generated just-infinite profinite branch group which is not positively finitely generated. ⋮ Embedding properties of hereditarily just infinite profinite wreath products ⋮ The Automaton Realization of Iterated Wreath Products of Cyclic Groups ⋮ The characterization by automata of certain profinite groups. ⋮ Hereditarily just infinite profinite groups with complete Hausdorff dimension spectrum ⋮ Characterization of finitely generated infinitely iterated wreath products

Cites Work

• Unnamed Item
• Simple groups, maximal subgroups, and probabilistic aspects of profinite groups
• The probability of generating certain profinite groups by two elements
• The probability of generating a finite classical group
• On the probability of generating a minimal d-generated group
• Maximal subgroups in finite and profinite groups
• Positively finitely generated groups

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