A note on a theorem of Megibben

Peter Danchev and Patrick Keef

Department of Mathematics, 127 SOU “I. N. Denkoglu” 43 Parchevich Street, Sofia 1000, Bulgaria
Department of Mathematics, Whitman College 63 Wolf Fock Place, Walla Walla, WA 99362, USA


Abstract: We prove that pure subgroups of thick Abelian $p$-groups which are modulo countable are again thick. This generalizes a result due to Megibben (Michigan Math. J. 1966). Some related results are also established.

AMSclassification: primary 20K10.

Keywords: thick groups, pure subgroups, countable extensions, divisible groups, bounded groups.