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Several elementary properties of the symmetric group [Formula: see text] extend in a nice way to the full transformation monoid [Formula: see text] of all maps of the set [Formula:… Click to show full abstract
Several elementary properties of the symmetric group [Formula: see text] extend in a nice way to the full transformation monoid [Formula: see text] of all maps of the set [Formula: see text] into itself. The group [Formula: see text] turns out to be the torsion part of the monoid [Formula: see text]. That is, there is a pretorsion theory in the category of all maps [Formula: see text], [Formula: see text] an arbitrary finite set, in which bijections are exactly the torsion objects.
Keywords:
properties symmetric;
pretorsion theory;
symmetric group;
formula see;
see text
Journal Title: Journal of Algebra and Its Applications
Year Published: 2019
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Journal Title: Journal of Algebra and Its Applications
Year Published: 2019
Link to full text (if available)
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recommendations!