Almost totally projective groups

Paul Hill; William Ullery

Displaying similar documents to “Almost totally projective groups”

The generalized criterion of Dieudonné for primary valuated groups

Peter Vassilev Danchev (2007)

Acta Mathematica Universitatis Ostraviensis

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On extensions of primary almost totally projective abelian groups

Peter Vassilev Danchev (2008)

Mathematica Bohemica

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Suppose $G$ is a subgroup of the reduced abelian $p$ -group $A$ . The following two dual results are proved: $(*)$ If $A / G$ is countable and $G$ is an almost totally projective group, then $A$ is an almost totally projective group. $(* *)$ If $G$ is countable and nice in $A$ such that $A / G$ is an almost totally projective group, then $A$ is an almost totally projective group. These results somewhat strengthen theorems due to Wallace (J. Algebra, 1971) and Hill (Comment. Math. Univ. Carol., 1995), respectively. ...

Isotype knice subgroups of global Warfield groups

Charles K. Megibben, William Ullery (2006)

Czechoslovak Mathematical Journal

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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 $H (ℵ_{0})$ -family of almost strongly separable $k$ -subgroups. By an $H (ℵ_{0})$ -family we mean an Axiom 3 family in the strong sense of P. Hill. As a corollary to the main theorem, we are able...