By Robert B. Warfield Jr. (auth.), David M. Arnold, Roger H. Hunter, Elbert A. Walker (eds.)

ISBN-10: 3540084479

ISBN-13: 9783540084471

ISBN-10: 3540370692

ISBN-13: 9783540370697

**Read Online or Download Abelian Group Theory: Proceedings of the 2nd New Mexico State University Conference, Held at Las Cruces, New Mexico, December 9–12, 1976 PDF**

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**Extra info for Abelian Group Theory: Proceedings of the 2nd New Mexico State University Conference, Held at Las Cruces, New Mexico, December 9–12, 1976**

**Example text**

I do not k n o w if this result can be s u b s t a n t i a l l y particular, T is simply presented. There is a c o u n t a b l y g e n e r a t e d torsion m o d u l e M @ T then the are equivalent: (i) (iv) [X] one can say more. following properties (iii) such that is totally projective. For c o u n t a b l y g e n e r a t e d modules p-local groups) [X] and such that one of the summands is that this is the w o r s t that can happen, 28 in the sense that any summand of a simply p r e s e n t e d m o d u l e is the direct sum of a simply p r e s e n t e d m o d u l e and a module of at most countable rank.

Subgroups functor In [48], in p-local M from mixed p-local subgroups, (Z(p)-modules) of finite rank. class. be developed globally (for mixed groups of finite rank)? then by an Ulm sequence mal torsion-free is reduced? , A/pA This gives a Can the corresponding subgroups if A (as in [48]) is cyclic). theory such that their are pure subgroups is one of these quasi-maximal of torsion- Can these groups be classified together with the isomorphism subgroups? ) somewhat weaker than the p-adic integers, Walker M ® Z~p) modules, quasi-maximal of finite rank Z~p) classes of finite rank torsion-free Problem 4.

Crawley and Hales [2] defined a class of groups now known as simply presented groups, and showed that a reduced p-group is simply presented if and only if it is totally projective. E. Walker [20] gave a new proof of Hill's theorem, generalizing it in a way significant to the study of mixed groups. In 1937, Baer [i] used a cardinal invariant called type to classify completely decomposable torsion-free groups. Baer also showed that direct summands of completely decomposable groups of finite rank are completely decomposable.

### Abelian Group Theory: Proceedings of the 2nd New Mexico State University Conference, Held at Las Cruces, New Mexico, December 9–12, 1976 by Robert B. Warfield Jr. (auth.), David M. Arnold, Roger H. Hunter, Elbert A. Walker (eds.)

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