Countable unions of totally projective groups
HTML articles powered by AMS MathViewer
- by Paul Hill PDF
- Trans. Amer. Math. Soc. 190 (1974), 385-391 Request permission
Abstract:
Let the p-primary abelian group G be the set-theoretic union of a countable collection of isotype subgroups ${H_n}$ of countable length. We prove that if ${H_n}$ is totally projective for each n, then G must be totally projective. In particular, an ascending sequence of isotype and totally projective subgroups of countable length leads to a totally projective group. The result generalizes and complements a number of theorems appearing in various articles in the recent literature. Several applications of the main result are presented.References
-
B. L. Edington, Isomorphic invariants in quotient categories of abelian groups, Dissertation, New Mexico State University, 1971.
- Phillip A. Griffith, Infinite abelian group theory, University of Chicago Press, Chicago, Ill.-London, 1970. MR 0289638
- Paul Hill, Isotype subgroups of direct sums of countable groups, Illinois J. Math. 13 (1969), 281β290. MR 240198
- Paul Hill, The purification of subgroups of abelian groups, Duke Math. J. 37 (1970), 523β527. MR 265456 β, On the classification of abelian groups, Xeroxed notes, 1967.
- Paul Hill, Primary groups whose subgroups of smaller cardinality are direct sums of cyclic groups, Pacific J. Math. 42 (1972), 63β67. MR 315018, DOI 10.2140/pjm.1972.42.63
- Paul Hill and Charles Megibben, On direct sums of countable groups and generalizations, Studies on Abelian Groups (Symposium, Montpellier, 1967) Springer, Berlin, 1968, pp.Β 183β206. MR 0242943 P. Hill and C. Megibben, On certain classes of primary abelian groups, Notices Amer. Math. Soc. 15 (1968), 105. Abstract #653-93.
- F. F. Kamalov, The subgroups of direct sums of countable abelian groups, Vestnik Moskov. Univ. Ser. I Mat. Meh. 26 (1971), no.Β 1, 31β35 (Russian, with English summary). MR 0280587
- Charles Megibben, The generalized Kulikov criterion, Canadian J. Math. 21 (1969), 1192β1205. MR 249509, DOI 10.4153/CJM-1969-132-9
- Charles Megibben, A generalization of the classical theory of primary groups, Tohoku Math. J. (2) 22 (1970), 347β356. MR 294491, DOI 10.2748/tmj/1178242761
- R. J. Nunke, On the structure of $\textrm {Tor}$. II, Pacific J. Math. 22 (1967), 453β464. MR 214659, DOI 10.2140/pjm.1967.22.453
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 190 (1974), 385-391
- MSC: Primary 20K10
- DOI: https://doi.org/10.1090/S0002-9947-1974-0338212-7
- MathSciNet review: 0338212