An extension of properties of symmetric group to monoids and a pretorsion theory in a category of mappings
2019 ◽
Vol 18
(12)
◽
pp. 1950234
◽
Keyword(s):
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.
1994 ◽
Vol 37
(3)
◽
pp. 471-476
◽
1982 ◽
Vol 33
(1)
◽
pp. 76-85
Keyword(s):
1982 ◽
Vol 23
(2)
◽
pp. 137-149
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2012 ◽
Vol 05
(03)
◽
pp. 1250035
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Keyword(s):
1978 ◽
Vol 81
(3-4)
◽
pp. 317-323
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Keyword(s):
2008 ◽
Vol 51
(1)
◽
pp. 57-72
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