Butler Theory over Murley Groups

A class of torsion-free abelian groups characterized by the ranks of their socles

“…The following appears in [3] in essence, however there is an error in the statement of Proposition 2.2 in [3], which is corrected here. Lemma 1.…”

Murley groups and the torsion-freeness of Ext

“…Theorem 2.4. The following conditions are equivalent for a reduced torsion-free group B of finite rank: a) B is a finitely faithful S-group such that, whenever U is a finite rank pure subgroup of a torsion-free group 1 1 ⊕ · · · ⊕ B m n n where B i is an irreducible Murley group for each i = 1, . .…”

“…Our results show that it is significantly more complex than the case OT(B) = type (Q). We want to remind the reader that the first author and Goeters showed in [1] that every irreducible Murley group B is of the form B = B τ ⊗ E where B τ is a rank-1 group of type τ and E = E(B) is the endomorphism ring of B. Moreover, E is a PID whose additive group E + is an irreducible Murley group too.…”