Glasnik Matematicki, Vol. 33, No.1 (1998), 13-17.

A NEW PROOF OF A THEOREM CONCERNING DECOMPOSABLE GROUPS

Wojciech Chojnacki

Instytut Matematyki Stosowanej i Mechanili, Uniwersytet Warszawski, ul. Banacha 2, 02-097 Warszawa, Poland
e-mail: wojtekch@appli.mimuw.edu.pl

Department of Computer Science, University of Adalaide, Adelaide, SA 5005, Australia
e-mail: wojtek@cs.adelaide.edu.au


Abstract.   We give an elementary proof of the following result: If G is a compact non-zero Abelian group with dual isomorphic to a subgroup of Q, such that U (-U) = G \ G(2) and U (-U) = Ø for some open subset U G, where G(2) = {a G : 2a = 0}, then G is topologically isomorphic with T.

1991 Mathematics Subject Classification.   22C05, 22B05.

Key words and phrases.   Compact, connected, decomposable, Abelian group.


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