ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Vol. LXXIV, 1 (2005)
p. 15 - 24
Generalized Dieudonne criterion
P. Danchev
Abstract.
An extension in the terms of $\sigma$-summable
abelian $p$-groups of the classical Dieudonn\'e criterion
(Portugaliae Mathematica, 1952) for direct sums of \hbox{$p$-cyclics} (= cyclic
$p$-groups) is given.
Specifically, it is proved that $G$ is a $\sigma$-summable abelian
$p$-group if $A$ is its balanced $\sigma$-summable
abelian $p$-subgroup so that $G/A$ is a \hbox{$\sigma$-summable}
abelian $p$-group.
In particular, some other well-known
results are also obtained.
AMS Subject classification: 20K10.
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