Showing papers on "Torsion-free abelian group published in 1983"
01 Jan 1983
TL;DR: In this article, it was shown that if G is a finite rank torsion free abelian group, then the following statements are equivalent: (i) G is pure subgroup of a finite-rank completely decomposable group C; (ii) g is a homomorphic image of D; and (iii) typeset(G) is finite and for each type τ, G(τ) = Gτ ⨁ *, for some τ-homogenous completely decompositionable group Gτ, and */G*(τ ) is finite.
Abstract: M. C. R. Butler, in 1965, proved that if G is a finite rank torsion free abelian group then the following statements are equivalent: (i) G is a pure subgroup of a finite rank completely decomposable group C; (ii) G is a homomorphic image of a finite rank completely decomposable group D; (iii) typeset(G) is finite and for each type τ, G(τ) = Gτ ⨁ *, for some τ-homogenous completely decomposable group Gτ, and */G*(τ) is finite.
49 citations
48 citations
01 Jan 1983
TL;DR: In this article, the authors studied the problem of realizing rational division algebras in a special way and showed that if p is a prime, D is p-realizable when there is a p-local torsion free abelian group A whose rank is the dimension of D over Q, such that D is isomorphic to the quasiendomorphism ring of A.
Abstract: In the paper [13], the authors studied the problem of realizing rational division algebras in a special way. Let D be a division algebra that is finite dimensional over the rational field Q. If p is a prime, we say that D is p-realizable when there is a p-local torsion free abelian group A whose rank is the dimension of D over Q, such that D is isomorphic to the quasiendomorphism ring of A.
10 citations
TL;DR: In this article, it was shown that the problem of finding necessary and sufficient conditions on two sets of types T such that T = typeset G, T' = cotypeset G for some rank two G of a group is NP-hard.
1 citations