Generating Countable Sets of Permutations | Zendy

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Generating Countable Sets of Permutations

Author(s) -

Galvin Fred

Publication year - 1995

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/jlms/51.2.230

Subject(s) - countable set , combinatorics , permutation group , permutation (music) , mathematics , generator (circuit theory) , symmetric group , property (philosophy) , group (periodic table) , set (abstract data type) , discrete mathematics , philosophy , physics , computer science , power (physics) , epistemology , quantum mechanics , programming language , aesthetics

Let E be an infinite set. In answer to a question of Wagon, I show that every countable subset of the symmetric group Sym( E ) is contained in a 2‐generator subgroup of Sym( E ). In answer to a question of Macpherson and Neumann, I show that, if Sym( E ) is generated by A ∪ B where | B | ⩽ ‖ E ‖, then Sym( E ) is generated by A ∪ {γ} for some permutation γ in Sym( E ).

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