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Endoprimal abelian groups

Part of: Algebraic structures Abelian groups

Published online by Cambridge University Press:  09 April 2009

Kalle Kaarli  and
László Márki
Kalle Kaarli
Affiliation:
Department of Mathematics University of TartuEE-50090 Tartu Estonia e-mail:kaarli@math.ut.ee
László Márki
Affiliation:
Mathematical Institute Hungarian Academy of SciencesH-1364 Budapest, Pf. 127 Hungary e-mail: marki@math-inst.hu
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Abstract

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A group A is said to be endoprimal if its term functions are precisely the functions which permute with all endomorphisms of A. In this paper we describe endoprimal groups in the following three classes of abelian groups: torsion groups, torsionfree groups of rank at most 2, direct sums of a torsion group and a torsionfree group of rank 1.

Keywords

abelian groupendoprimal

MSC classification

Secondary: 20K30: Automorphisms, homomorphisms, endomorphisms, etc. 20K99: None of the above, but in this section 20K25: Direct sums, direct products, etc. 08A40: Operations, polynomials, primal algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 67 , Issue 3 , December 1999 , pp. 412 - 428
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Baer, R., ‘The subgroup of the elements of finite order of an abelian group’, Ann. of Math. 37 (1936), 766–781.CrossRefGoogle Scholar
[2]Davey, B. A., ‘Duality for equational classes of Brouwerian and Heyting algebras’, Trans. Amer. Math. Soc. 221 (1976), 119–146.CrossRefGoogle Scholar
[3]Davey, B. A., ‘Dualisability in general and endodualisability in particular’, in: Logic and algebra, Lecture Notes in Pure and Appl. Math. 180 (Marcel Dekker, New York, 1996), pp. 437–455.Google Scholar
[4]Davey, B. A. and Pitkethly, J. G., ‘Endoprimal algebras’, Algebra Universalis 38 (1997), 266–288.CrossRefGoogle Scholar
[5]Davey, B. A. and Werner, H., ‘Piggyback-Dualitäten’, Bull. Austral. Math. Soc. 32 (1985), 1–32.CrossRefGoogle Scholar
[6]Fomin, S. V., ‘Über periodische Untergruppen der unendlichen abelschen Gruppen’, Mat. Sb. 2 (1937), 1007–1009.Google Scholar
[7]Fuchs, L., Infinite abelian groups, I–II (Academic Press, New York, 1970, 1973).Google Scholar
[8]Kaarli, K., ‘Affine complete Abelian groups’, Math. Nachr. 107 (1982), 235–239.CrossRefGoogle Scholar
[9]Márki, L. and Pöschel, R., ‘Endoprimal distributive lattices’, Algebra Universalis 30 (1993), 272–274.CrossRefGoogle Scholar