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Endoprimal Abelian
Groups
Laszlo
Marki
Alfred Renyi
Institute of Mathematics
Hungarian
Academy of Sciences, Budapest
An
algebra is said to be endoprimal if all those finitary functions in it
which permute with every endomorphism of the algebra are term functions
- in the case of abelian groups the latter means the functions of the
form with
integers .
First results on endoprimality of abelian groups have shown a close
connection of endoprimality to decomposition properties including, among
others, a complete description of endoprimal torsion groups. Here we
present recent results by K. Kaarli, L. Marki and further coauthors
which solve the problem of endoprimality for separable torsion-free
abelian groups, torsion-free abelian groups of rank 3, and mixed abelian
groups of torsion-free rank 1.
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