A new characterization for $p$-local balanced projective groups
Author:
Mark Lane
Journal:
Proc. Amer. Math. Soc. 96 (1986), 379-386
MSC:
Primary 20K21; Secondary 20K10
DOI:
https://doi.org/10.1090/S0002-9939-1986-0822423-1
MathSciNet review:
822423
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: By introducing the notion of a ${\text {K}}$-nice submodule, we obtain a characterization of $p$-local balanced projectives perfectly analogous to the familiar third axiom of countability characterization of totally projective $p$-groups. We use this new characterization to prove that if a $p$-local group $G$ satisfies the third axiom of countability with respect to nice submodules and has a ${\text {K}}$-basis, then $G$ is a balanced projective.
- LΓ‘szlΓ³ Fuchs, Infinite abelian groups. Vol. II, Academic Press, New York-London, 1973. Pure and Applied Mathematics. Vol. 36-II. MR 0349869 P. Hill, On the classification of abelian groups, photocopied manuscript.
- Paul Hill, Isotype subgroups of totally projective groups, Abelian group theory (Oberwolfach, 1981) Lecture Notes in Math., vol. 874, Springer, Berlin-New York, 1981, pp. 305β321. MR 645937
- Roger Hunter and Fred Richman, Global Warfield groups, Trans. Amer. Math. Soc. 266 (1981), no. 2, 555β572. MR 617551, DOI https://doi.org/10.1090/S0002-9947-1981-0617551-X
- Fred Richman, The constructive theory of $KT$-modules, Pacific J. Math. 61 (1975), no. 1, 263β274. MR 399069
- Fred Richman and Elbert A. Walker, Valuated groups, J. Algebra 56 (1979), no. 1, 145β167. MR 527162, DOI https://doi.org/10.1016/0021-8693%2879%2990330-2
- Elbert A. Walker, Ulmβs theorem for totally projective groups, Proc. Amer. Math. Soc. 37 (1973), 387β392. MR 311805, DOI https://doi.org/10.1090/S0002-9939-1973-0311805-3
- R. B. Warfield Jr., A classification theorem for abelian $p$-groups, Trans. Amer. Math. Soc. 210 (1975), 149β168. MR 372071, DOI https://doi.org/10.1090/S0002-9947-1975-0372071-2
- R. B. Warfield Jr., Classification theory of abelian groups. I. Balanced projectives, Trans. Amer. Math. Soc. 222 (1976), 33β63. MR 422455, DOI https://doi.org/10.1090/S0002-9947-1976-0422455-X
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Additional Information
Keywords:
Balanced projective groups,
<!β MATH ${\text {K}}$ β> <IMG WIDTH="21" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${\text {K}}$">-module,
<!β MATH ${\text {K}}$ β> <IMG WIDTH="21" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img3.gif" ALT="${\text {K}}$">-nice,
third axiom of countability,
Ulm invariants,
<IMG WIDTH="17" HEIGHT="19" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$h$">-invariants
Article copyright:
© Copyright 1986
American Mathematical Society
