Growth of linear semigroups
1996 ◽
Vol 60
(1)
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pp. 18-30
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Keyword(s):
AbstractWe show that the growth function of a finitely generated linear semigroup S ⊆ Mn(K) is controlled by its behaviour on finitely many cancellative subsemigroups of S. If the growth of S is polynomially bounded, then every cancellative subsemigroup T of S has a group of fractions G ⊆ Mn (K) which is nilpotent-by-finite and of finite rank. We prove that the latter condition, strengthened by the hypothesis that every such G has a finite unipotent radical, is sufficient for S to have a polynomial growth. Moreover, the degree of growth of S is then bounded by a polynomial f(n, r) in n and the maximal degree r of growth of finitely generated cancellative T ⊆ S.
2008 ◽
Vol 18
(01)
◽
pp. 59-82
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1996 ◽
Vol 06
(03)
◽
pp. 369-377
2009 ◽
Vol 1
(3)
◽
pp. 537-546
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1988 ◽
Vol 31
(3)
◽
pp. 374-379
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1987 ◽
Vol 36
(1)
◽
pp. 153-160
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Keyword(s):
2013 ◽
Vol 44
(4)
◽
pp. 417-432
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2017 ◽
Vol 166
(1)
◽
pp. 83-121
Keyword(s):
2003 ◽
Vol 13
(05)
◽
pp. 565-583
◽
Keyword(s):
2007 ◽
Vol 17
(08)
◽
pp. 1611-1634
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Keyword(s):
1985 ◽
Vol 98
(3)
◽
pp. 437-445
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Keyword(s):