Classes of universal words for the infinite symmetric groups

DOI10.1007/BF01278598zbMath0569.20005MaRDI QIDQ1061218

Manfred Droste

Publication date: 1985

Published in: Algebra Universalis (Search for Journal in Brave)

zbMATH Keywords

infinite symmetric groupsISym-universal wordsJordan-Hölder decomposition seriessimple factor-groupsverbally completeZ-universal words

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Symmetric groups (20B30)

Related Items (10)

Representations of Infinite Permutations by Words ⋮ Cubes of Conjugacy Classes Covering the Infinite Symmetric Group ⋮ On generating sets of infinite symmetric group ⋮ On Ore’s Theorem and Universal Words for Permutations and Injections of Infinite Sets ⋮ On the Universality of Words for the Alternating Groups ⋮ Squares of Conjugacy Classes in the Infinite Symmetric Groups ⋮ Sets of universal sequences for the symmetric group and analogous semigroups ⋮ The reverse spelling of an FPrt-universal word in two letters ⋮ Products of Involution Classes in Infinite Symmetric Groups ⋮ The equation \(s=(x^ 2y^ 2)^ 3y^ 2\) is solvable in the symmetric group on Z

Cites Work

• On a theorem of Baer, Schreier, and Ulam for permutations
• Products of conjugacy classes of the infinite symmetric groups
• On the universality of systems of words in permutation groups
• Products of conjugate permutations
• Universal terms of the form \(B^nA^m\)
• Representations of Infinite Permutations by Words
• Some Constructions for Locally Finite Groups
• Are Primitive Words Universal for Infinite Symmetric Groups?
• Equations in groups
• Can One Solve Equations in Group?
• Equations Unsolvable in GL 2 (C) and Related Problems
• Some Remarks on Commutators

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