BREAKING UP FINITE AUTOMATA PRESENTABLE TORSION-FREE ABELIAN GROUPS
2011 ◽
Vol 21
(08)
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pp. 1463-1472
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Keyword(s):
In [Todor Tsankov, The additive group of the rationals does not have an automatic presentation, May 2009, arXiv:0905.1505v1], it was shown that the group of rational numbers is not FA-presentable, i.e. it does not admit a presentation by a finite automaton. More generally, any torsion-free abelian group that is divisible by infinitely many primes is not of this kind. In this article we extend the result from [13] and prove that any torsion-free FA-presentable abelian group G is an extension of a finite rank free group by a finite direct sum of Prüfer groups ℤ(p∞).
1992 ◽
Vol 52
(2)
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pp. 219-236
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Keyword(s):
1996 ◽
Vol 48
(5)
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pp. 918-929
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Keyword(s):
1989 ◽
Vol 39
(1)
◽
pp. 21-24
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Keyword(s):
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2016 ◽
Vol 94
(3)
◽
pp. 449-456
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Keyword(s):
2000 ◽
Vol 20
(4)
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pp. 1111-1125
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1993 ◽
Vol 54
(2)
◽
pp. 143-155
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Keyword(s):