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Isotype knice subgroups of global Warfield groups

Charles K. MegibbenWilliam Ullery — 2006

Czechoslovak Mathematical Journal

If H is an isotype knice subgroup of a global Warfield group G , we introduce the notion of a k -subgroup to obtain various necessary and sufficient conditions on the quotient group G / H in order for H itself to be a global Warfield group. Our main theorem is that H is a global Warfield group if and only if G / H possesses an H ( 0 ) -family of almost strongly separable k -subgroups. By an H ( 0 ) -family we mean an Axiom 3 family in the strong sense of P. Hill. As a corollary to the main theorem, we are able to characterize...

Isotype subgroups of mixed groups

Charles K. MegibbenWilliam Ullery — 2001

Commentationes Mathematicae Universitatis Carolinae

In this paper, we initiate the study of various classes of isotype subgroups of global mixed groups. Our goal is to advance the theory of Σ -isotype subgroups to a level comparable to its status in the simpler contexts of torsion-free and p -local mixed groups. Given the history of those theories, one anticipates that definitive results are to be found only when attention is restricted to global k -groups, the prototype being global groups with decomposition bases. A large portion of this paper is...

The nonseparability of simply presented mixed groups

Paul HillCharles K. Megibben — 1998

Commentationes Mathematicae Universitatis Carolinae

It is demonstrated that an isotype subgroup of a simply presented abelian group can be simply presented without being a separable subgroup. In particular, the conjecture based on a variety of special cases that Warfield groups are absolutely separable is disproved.

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