Are Primitive Words Universal for Infinite Symmetric Groups?

DOI10.2307/1999086zbMath0514.20022OpenAlexW4235789831MaRDI QIDQ3659972

Donald Silberger

Publication date: 1983

Full work available at URL: https://doi.org/10.2307/1999086

zbMATH Keywords

primitive wordsequations in groupsinfinite symmetric groupsuniversal words in groups

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Symmetric groups (20B30)

Related Items

Even permutations as a product of two elements of order five ⋮ Representations of Infinite Permutations by Words ⋮ Representation of Tree Permutations by Words ⋮ On the Universality of Words for the Alternating Groups ⋮ Sets of universal sequences for the symmetric group and analogous semigroups ⋮ The reverse spelling of an FPrt-universal word in two letters ⋮ Classes of universal words for the infinite symmetric groups ⋮ The equation \(s=(x^ 2y^ 2)^ 3y^ 2\) is solvable in the symmetric group on Z

Cites Work

• Unnamed Item
• On a theorem of Baer, Schreier, and Ulam for permutations
• Periodicity and unbordered segments of words
• Universal terms of the form \(B^nA^m\)
• Some problems on the universality of words in groups
• Permutations as products of conjugate infinite cycles
• Even permutations as a product of two conjugate cycles
• Equations in groups
• Can One Solve Equations in Group?
• Equations Unsolvable in GL 2 (C) and Related Problems
• Some Remarks on Commutators
• Ramified coverings of Riemann surfaces