Geodesic
Isotype knice subgroups of global Warfield groups
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 1, pp. 109-132.

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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 $H(\aleph _0)$-family of almost strongly separable $k$-subgroups. By an $H(\aleph _0)$-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 those global $k$-groups of sequentially pure projective dimension $\le 1$.
Classification : 20K21, 20K27
Keywords: global Warfield group; isotype subgroup; knice subgroup; $k$-subgroup; separable subgroup; compatible subgroups; Axiom 3; closed set method; global $k$-group; sequentially pure projective dimension 
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     author = {Megibben, Charles and Ullery, William},
     title = {Isotype knice subgroups of global {Warfield} groups},
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Megibben, Charles; Ullery, William. Isotype knice subgroups of global Warfield groups. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 1, pp. 109-132. http://geodesic.mathdoc.fr/item/CMJ_2006__56_1_a8/