Isotype knice subgroups of global Warfield groups

Charles K. Megibben; William Ullery

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 1, page 109-132
  • ISSN: 0011-4642

Abstract

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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 to characterize those global k -groups of sequentially pure projective dimension ≤ 1 .

How to cite

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Megibben, Charles K., and Ullery, William. "Isotype knice subgroups of global Warfield groups." Czechoslovak Mathematical Journal 56.1 (2006): 109-132. <http://eudml.org/doc/31020>.

@article{Megibben2006,
abstract = {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 $\le 1$.},
author = {Megibben, Charles K., Ullery, William},
journal = {Czechoslovak Mathematical Journal},
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; global Warfield groups; isotype subgroups; knice subgroups; separable subgroups; compatible subgroups; Axiom 3; sequentially pure projective dimension; -subgroups},
language = {eng},
number = {1},
pages = {109-132},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Isotype knice subgroups of global Warfield groups},
url = {http://eudml.org/doc/31020},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Megibben, Charles K.
AU - Ullery, William
TI - Isotype knice subgroups of global Warfield groups
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 1
SP - 109
EP - 132
AB - 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 $\le 1$.
LA - eng
KW - 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; global Warfield groups; isotype subgroups; knice subgroups; separable subgroups; compatible subgroups; Axiom 3; sequentially pure projective dimension; -subgroups
UR - http://eudml.org/doc/31020
ER -

References

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