Isotype knice subgroups of global Warfield groups

Megibben, Charles ; Ullery, William

Czechoslovak Mathematical Journal, Tome 56 (2006) no. 1, pp. 109-132.

Résumé

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 $H({\mathrm{\aleph }}_0)$-family of almost strongly separable $k$-subgroups. By an $H({\mathrm{\aleph }}_0)$-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 $\le 1$.

Détail

Classification : 20K21, 20K27
Mots-clés : 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