Growth sequences of finite semigroups
1987 ◽
Vol 43
(1)
◽
pp. 16-20
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Keyword(s):
AbstractThe growth sequence of a finite semigroup S is the sequence {d(Sn)}, where Sn is the nth direct power of S and d stands for minimum generating number. When S has an identity, d(Sn) = d(Tn) + kn for all n, where T is the group of units and k is the minimum number of generators of S mod T. Thus d(Sn) is essentially known since d(Tn) is (see reference 4), and indeed d(Sn) is then eventually piecewise linear. On the other hand, if S has no identity, there exists a real number c > 1 such that d(Sn) ≥ cn for all n ≥ 2.
1981 ◽
Vol 31
(3)
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pp. 374-375
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Keyword(s):
1974 ◽
Vol 17
(2)
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pp. 133-141
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1993 ◽
Vol 123
(5)
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pp. 839-855
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2002 ◽
Vol 12
(01n02)
◽
pp. 137-178
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Keyword(s):
1989 ◽
Vol 40
(2)
◽
pp. 323-329
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Keyword(s):
Keyword(s):
1990 ◽
Vol 48
(1)
◽
pp. 87-88
◽
2008 ◽
Vol 2008
◽
pp. 1-5
Keyword(s):