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Maximal Subgroups of Infinite Symmetric Groups
Author(s) -
Macpherson H. D.,
Praeger Cheryl E.
Publication year - 1990
Publication title -
journal of the london mathematical society
Language(s) - Uncategorized
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-42.1.85
Subject(s) - countable set , permutation group , mathematics , combinatorics , symmetric group , maximal subgroup , transitive relation , group (periodic table) , cyclic permutation , permutation (music) , normal subgroup , index of a subgroup , set (abstract data type) , characteristic subgroup , discrete mathematics , physics , computer science , quantum mechanics , acoustics , programming language
It is shown that if G is a permutation group on a countable set X and if G is not highly transitive, then G is contained in some maximal proper subgroup of the full symmetric group on X .