Ulm’s theorem for totally projective groups

Walker, Elbert A.

doi:10.1090/S0002-9939-1973-0311805-3

Ulm’s theorem for totally projective groups
HTML articles powered by AMS MathViewer

by Elbert A. Walker

Proc. Amer. Math. Soc. 37 (1973), 387-392

DOI: https://doi.org/10.1090/S0002-9939-1973-0311805-3

PDF | Request permission

Abstract:

This paper simplifies the proof of Hill’s version of Ulm’s theorem for totally projective groups by giving one which in essence is the same as the Mackey proof for the countable case.

References

Peter Crawley and Alfred W. Hales, The structure of torsion abelian groups given by presentations, Bull. Amer. Math. Soc. 74 (1968), 954–956. MR 232840, DOI 10.1090/S0002-9904-1968-12102-0
Peter Crawley and Alfred W. Hales, The structure of abelian $p$-groups given by certain presentations, J. Algebra 12 (1969), 10–23. MR 238947, DOI 10.1016/0021-8693(69)90014-3
L. Fuchs, Abelian groups, International Series of Monographs on Pure and Applied Mathematics, Pergamon Press, New York-Oxford-London-Paris, 1960. MR 0111783
Phillip A. Griffith, Infinite abelian group theory, University of Chicago Press, Chicago, Ill.-London, 1970. MR 0289638

On the classification of abelian groups

Ulm’s theorem for totally projective groups

14

Irving Kaplansky, Infinite abelian groups, Revised edition, University of Michigan Press, Ann Arbor, Mich., 1969. MR 0233887
George Kolettis Jr., Direct sums of countable groups, Duke Math. J. 27 (1960), 111–125. MR 110748
R. J. Nunke, Homology and direct sums of countable abelian groups, Math. Z. 101 (1967), 182–212. MR 218452, DOI 10.1007/BF01135839
Larry D. Parker and Elbert A. Walker, An extension of the Ulm-Kolettis theorems, Studies on Abelian Groups (Symposium, Montpellier, 1967) Springer, Berlin, 1968, pp. 309–325. MR 0265458
Helmut Ulm, Zur Theorie der abzählbar-unendlichen Abelschen Gruppen, Math. Ann. 107 (1933), no. 1, 774–803 (German). MR 1512826, DOI 10.1007/BF01448919