Extensions of Nice Bases on ULM Subgroups of Primary Abelian Groups With Totally Projective Quotients
DOI:
https://doi.org/10.5644/SJM.09.2.03Keywords:
Primary Abelian groups, nice bases, totally projective groups, Ulm subgroups, Ulm factorsAbstract
Suppose $G$ is an abelian $p$-group, $\alpha$ is an ordinal and $G/p^\alpha$$G$ is totally projective. We show that $G$ has a nice basis if and only if $G/p^\alpha$$G$ has a nice basis. This extends results of Danchev in Bull. Malaysian Math. Sci. Soc. (2010), Bull. Allah. Math. Soc. (2011) and An. St. Univ. Ovidius Constanta (2012), as well as joint work with Keef in Rocky Mount. J. Math. (2011).
2010 Mathematics Subject Classification. 20K10.
Downloads
References
P. V. Danchev, Nice bases for mixed and torsion-free abelian groups, Bull. Malays. Math. Sci. Soc., 33 (3) (2010), 393–403.
P. V. Danchev, Extending nice bases on Ulm subgroups of abelian p-groups, Bull. Allah. Math. Soc., 26 (2) (2011), 225–228.
P. V. Danchev, An extension of nice bases on Ulm subgroups of primary abelian groups, An. St. Univ. Ovidius Constanta, 20 (3) (2012), 33–36.
P. V. Danchev and B. Goldsmith, On socle-regularity and some notions of transitivity for abelian p-groups, J. Comm. Algebra, 3 (3) (2011), 301–319.
P. V. Danchev and P. W. Keef, Nice bases and thickness in primary abelian groups, Rocky Mount. J. Math., 41 (4) (2011), 1127–1149.
L. Fuchs, Infinite Abelian Groups, Volumes I and II, Acad. Press, New York and London, 1970 and 1973.
P. D. Hill, On transitive and fully transitive primary groups, Proc. Amer. Math. Soc., 22 (2) (1969), 414–417.
