| Title:
|
Isotype knice subgroups of global Warfield groups (English) |
| Author:
|
Megibben, Charles |
| Author:
|
Ullery, William |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
109-132 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $\le 1$. (English) |
| Keyword:
|
global Warfield group |
| Keyword:
|
isotype subgroup |
| Keyword:
|
knice subgroup |
| Keyword:
|
$k$-subgroup |
| Keyword:
|
separable subgroup |
| Keyword:
|
compatible subgroups |
| Keyword:
|
Axiom 3 |
| Keyword:
|
closed set method |
| Keyword:
|
global $k$-group |
| Keyword:
|
sequentially pure projective dimension |
| MSC:
|
20K21 |
| MSC:
|
20K27 |
| idZBL:
|
Zbl 1157.20028 |
| idMR:
|
MR2206290 |
| . |
| Date available:
|
2009-09-24T11:31:57Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128057 |
| . |
| Reference:
|
[1] U. Albrecht and P. Hill: Butler groups of infinite rank and axiom 3.Czechoslovak Math. J. 37 (1987), 293–309. MR 0882600 |
| Reference:
|
[2] L. Fuchs: Infinite Abelian Groups.Vol. II, Academic Press, New York, 1973. Zbl 0257.20035, MR 0349869 |
| Reference:
|
[3] L. Fuchs and P. Hill: The balanced projective dimension of abelian $p$-groups.Trans. Amer. Math. Soc. 293 (1986), 99–112. MR 0814915 |
| Reference:
|
[4] L. Fuchs and M. Magidor: Butler groups of arbitrary cardinality.Israel J. Math. 84 (1993), 239–263. MR 1244670, 10.1007/BF02761702 |
| Reference:
|
[5] P. Hill: The third axiom of countability for abelian groups.Proc. Amer. Math. Soc. 82 (1981), 347–350. Zbl 0467.20041, MR 0612716, 10.1090/S0002-9939-1981-0612716-0 |
| Reference:
|
[6] P. Hill: Isotype subgroups of totally projective groups.Lecture Notes in Math vol. 874, Springer-Verlag, New York, 1981, pp. 305–321. Zbl 0466.20028, MR 0645937 |
| Reference:
|
[7] P. Hill and C. Megibben: Knice subgroups of mixed groups.Abelian Group Theory, Gordon-Breach, New York, 1987, pp. 89–109. MR 1011306 |
| Reference:
|
[8] P. Hill and C. Megibben: Mixed groups.Trans. Amer. Math. Soc. 334 (1992), 121–142. MR 1116315, 10.1090/S0002-9947-1992-1116315-8 |
| Reference:
|
[9] P. Hill and C. Megibben: The nonseparability of simply presented mixed groups.Comment. Math. Univ. Carolinae 39 (1998), 1–5. MR 1622308 |
| Reference:
|
[10] P. Hill and W. Ullery: Isotype subgroups of local Warfield groups.Comm. Algebra 29 (2001), 1899–1907. MR 1837949 |
| Reference:
|
[11] C. Megibben and W. Ullery: Isotype subgroups of mixed groups.Comment. Math. Univ. Carolinae 42 (2001), 421–442. MR 1859590 |
| Reference:
|
[12] C. Megibben and W. Ullery: Isotype Warfield subgroups of global Warfield groups.Rocky Mountain J. Math. 32 (2002), 1523–1542. MR 1987623, 10.1216/rmjm/1181070038 |
| Reference:
|
[13] R. Warfield: Simply presented groups.Proc. Sem. Abelian Group Theory, Univ. of Arizona lecture notes, 1972. |
| . |
