Generating the infinite symmetric group using a closed subgroup and the least number of other elements

DOI10.1090/S0002-9939-2010-10694-9zbMath1229.20004OpenAlexW2073836366MaRDI QIDQ3082309

Michał Morayne, James D. Mitchell, Yann Peresse

Publication date: 10 March 2011

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-2010-10694-9

zbMATH Keywords

generatorssubgroupsPolish groupsinfinite symmetric grouppermutation groups on countably infinite setcardinalities of orbits

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Topological groups (topological aspects) (54H11) General theory for infinite permutation groups (20B07) Cardinal characteristics of the continuum (03E17) Symmetric groups (20B30)

Related Items (1)

On the semigroup rank of a group

Cites Work

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• Generating transformation semigroups using endomorphisms of preorders, graphs, and tolerances.
• Set theory. An introduction to independence proofs. 2nd print
• Closed subgroups of the infinite symmetric group.
• Generating self-map monoids of infinite sets.
• The Cichoń diagram
• Generating continuous mappings with Lipschitz mappings
• Turbulence, amalgamation, and generic automorphisms of homogeneous structures
• Subgroups of Infinite Symmetric Groups
• On relative ranks of full transformation semigroups
• Generating Countable Sets of Permutations
• Endomorphism rings generated using small numbers of elements

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