Idempotent generators in finite full transformation semigroups
1978 ◽
Vol 81
(3-4)
◽
pp. 317-323
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Keyword(s):
SynopsisIt was proved by Howie in 1966 that , the semigroup of all singular mappings of a finite set X into itself, is generated by its idempotents. Implicit in the method of proof, though not formally stated, is the result that if |X| = n then the n(n – 1) idempotents whose range has cardinal n – 1 form a generating set for. Here it is shown that if n ≧ 3 then a minimal set M of idempotent generators for contains ½n(n–1) members. A formula is given for the number of distinct sets M.
1990 ◽
Vol 114
(3-4)
◽
pp. 161-167
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1982 ◽
Vol 23
(2)
◽
pp. 137-149
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2016 ◽
Vol 16
(07)
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pp. 1750138
Keyword(s):
2012 ◽
Vol 05
(03)
◽
pp. 1250035
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1988 ◽
Vol 30
(2)
◽
pp. 203-211
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1990 ◽
Vol 115
(3-4)
◽
pp. 289-299
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2015 ◽
Vol 25
(08)
◽
pp. 1187-1222
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Keyword(s):