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Monoids of injective maps closed under conjugation by permutations. (English) Zbl 1263.20060

The author classifies all transformation monoids consisting of injective transformations of a countable set and satisfying the condition that they are closed under conjugation by bijective transformations.

MSC:

20M20 Semigroups of transformations, relations, partitions, etc.
20B07 General theory for infinite permutation groups
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References:

[1] R. Baer, Die Kompositionsreihe der Gruppe aller eineindeutigen Abbildungen einer unendlichen Menge auf sich, Studies in Mathematics 5 (1934), 15–17. · JFM 60.0892.03
[2] E. A. Bertram, On a theorem of Schreier and Ulam for countable permutations, Journal of Algebra 24 (1973), 316–322. · Zbl 0257.05005
[3] A. H. Clifford and G. B. Preston, Algebraic Theory of Semigroups, Vol. II, Math. Surveys No. 7, American Mathematical Society, Providence, RI, 1967. · Zbl 0178.01203
[4] M. Droste and R. Göbel, On a theorem of Baer, Schreier, and Ulam for permutations, Journal of Algebra 58 (1979), 282–290. · Zbl 0416.20001
[5] R. Gilmer, Commutative Semigroup Rings, University Chicago Press, Chicago, 1984.
[6] D. Lindsey and B. Madison, The lattice of congruences on a Baer-Levi semigroup, Semigroup Forum 12 (1976), 63–70. · Zbl 0321.20045
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[8] J. Schreier and S. Ulam, Über die Permutationsgruppe der natürlichen Zahlenfolge, Studies in Mathematics 4 (1933), 134–141. · Zbl 0008.20003
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