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Rendiconti del Seminario Matematico della Università di Padova


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Volume 144, 2020, pp. 177–195
DOI: 10.4171/RSMUP/64

Published online: 2020-12-10

Free subgroups with torsion quotients and profinite subgroups with torus quotients

Wayne Lewis[1], Peter Loth[2] and Adolf Mader[3]

(1) University of Hawai‘i, Honolulu, USA
(2) Sacred Heart University, Fairfield, USA
(3) University of Hawai‘i at Mānoa, Honolulu, USA

Here “group” means abelian group. Compact connected groups contain $\delta$-subgroups, that is, compact totally disconnected subgroups with torus quotients, which are essential ingredients in the important Resolution Theorem, a description of compact groups. Dually, full free subgroups of discrete torsion-free groups of finite rank are studied in order to obtain a comprehensive picture of the abundance of $\delta$-subgroups of a protorus. Associated concepts are also considered.

Keywords: Torsion-free abelian group, finite rank, full free subgroup, Pontryagin Duality, compact abelian group, totally disconnected, profinite, torus quotient, Resolution Theorem

Lewis Wayne, Loth Peter, Mader Adolf: Free subgroups with torsion quotients and profinite subgroups with torus quotients. Rend. Sem. Mat. Univ. Padova 144 (2020), 177-195. doi: 10.4171/RSMUP/64