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Extra info for Abelian Group Theory: Proceedings of the Oberwolfach Conference, January 12–17, 1981

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F [3]). groups In p a r t i c u l a r , then the class isomorphism. N-group isomorphic if w h e n e v e r to A then B is a f i n i t e B rank is i s o m o r p h i c to A. 6: Suppose quasi-isomorphic free group. to an Then the that A N-group, following is a B u t l e r and t h a t are group, B equivalent: A is is a f i n i t e rank torsion 18 (a) A • D [ B • D (b) A (c) A @ C ~ B @ C Proof: C is an f(B)] (b) (c) Let is f i n i t e for is n e a r l y and The primes (a) p E(A)/NE(A) D; B; N-group C quasi-isomorphic D.

4). Again is a l m o s t completely decomposable. [i], is q u a s i - i s o m o r p h i c by the + preceding (~) (R/NR) + remarks, (R/NR) By Beaumont-Pierce so t h a t R+ is a B u t l e r R+ group. 2: completely A algebra group free of (~) since decomposable Hom(A,Z) ring with A R if (E(A)/NE(A)) + quasi-equal hence group. = 0 - Hom(Z,A) group then Furthermore, then (a) is q u a s i - i s o m o r p h i c , with is a B u t l e r decomposable. is a s i m p l e R+ completely is a B u t l e r rank torsion proof then c R = E(ZeA) (NR) +.

Group we mean subgroup of Proposition balanced This 12: . the groups >, = < B*(T) if d(B) Clearly B is a r a n k B n C*(7 i group ) ~ < B*(T 0 ) >, 0 g r o u p A, torsionfree Here, group these [2] w h i c h there subgroups are pure rank. completely a completely are Butler of subgroups [i] a n d is a b a l a n c e d of f i n i t e containing groups of A. D. A r n o l d b y an a l m o s t *-balanced sequence subgroup *-balanced groups. decomposable below. Clearly, exact the groups decomposable to e a c h B u t l e r rank An between a n d the B u t l e r C is c o m p l e t e l y index.

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