A THEOREM ON MATRIX GROUPS
2008 ◽
Vol 18
(01)
◽
pp. 165-180
Keyword(s):
Let K be a principal ideal domain, and An, with n ≥ 3, be a finitely generated torsion-free abelian group of rank n. Let Ω be a finite subset of KAn\{0} and U(KAn) the group of units of KAn. For a multiplicative monoid P generated by U(KAn) and Ω, we prove that any generating set for [Formula: see text] contains infinitely many elements not in [Formula: see text]. Furthermore, we present a way of constructing elements of [Formula: see text] not in [Formula: see text] for n ≥ 3. In the case where K is not a field the aforementioned results hold for n ≥ 2.
On Determinability of a Completely Decomposable Torsion-Free Abelian Group by its Automorphism Group
2018 ◽
Vol 230
(3)
◽
pp. 372-376
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Keyword(s):
Keyword(s):
1992 ◽
Vol 52
(2)
◽
pp. 219-236
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Keyword(s):
Keyword(s):
Keyword(s):
Keyword(s):
1989 ◽
Vol 39
(1)
◽
pp. 21-24
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Keyword(s):
Keyword(s):
1990 ◽
Vol 18
(9)
◽
pp. 2841-2883
◽
Keyword(s):
2011 ◽
Vol 21
(08)
◽
pp. 1463-1472
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