p. 85 - 91 Generalized Dieudonne and Honda criteria for primary Abelian groups P. V. Danchev Received: November 02, 2006; Accepted: April 13, 2007 Abstract. We prove two theorems of the type of Dieudonne for the classes of p-torsion n-Σ-groups and weakly n-summable groups, respectively. These claims extend the classical Dieudonne criterion (Portugal. Math., 1952) and Honda criterion (Comment. Math. Univ. St. Pauli, 1964) as well as generalize recent results of ours in (Acta Math. Univ. Ostrav., 2006; 2007) and (Alg. Colloq., 2008). Keywords: abelian groups, n-Σ-groups; weakly n-summable groups; height-finite subgroups; countable ascending unions. AMS Subject classification: Primary: 20K10. PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2008, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |