# Article

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Keywords:
completely subdirect product; convergence $\ell$-group; $b$-sequential compactness
Summary:
In this paper we investigate abelian convergence $\ell$-groups with zero radical such that each bounded sequence has a convergent subsequence.
References:
[1] P. Conrad: Lateral completion of lattice ordered groups. Proc. London Math. Soc. 19 (1969), 444-480. DOI 10.1112/plms/s3-19.3.444 | MR 0244125
[2] P. Conrad: Lattice ordered groups. Tulane University, 1970. Zbl 0258.06011
[3] D. N. Dikranjan: Convergence groups: sequential compactness and generalizations. Rendinconti 1st. Math. Trieste 25 (1993), 141-173. MR 1346320 | Zbl 0846.54033
[4] M. Harminc: Sequential convergences on abelian lattice ordered groups. Convergence Structures, Proc. Conf. Bechyne 1984, Math. Research 24 (1984), 153-158. MR 0835480
[5] M. Harminc J. Jakubík: Maximal convergences and minimal proper convergences in l-groups. Czechoslovak Math. J. 39 (1989), 631-640. MR 1017998
[6] J. Jakubík: Sequential convergences in l-groups without Urysohn's axiom. Czechoslovak Math. J. 42 (1992), 101-116. MR 1152174 | Zbl 0770.06008
[7] F. Šik: Über subdirekte Summen geordneter Gruppen. Czechoslovak Math. J. 10 (1960), 400-424. MR 0123626

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