A Basis Theorem for Subgroups of Bounded Abelian Groups
In this paper we present a generalization of the main aspects of the basis theorem for pairs (G,H) in which H is a subgroup of a finite abelian group G, see , to the case in which G is an abelian group of bounded order. The proof we outline here is actually simpler than the one sketched in . We remark that the assumption of the well ordering principle which occurs in the statement of the theorem is not an essential feature of it.
KeywordsAbelian Group Induction Hypothesis Basis Element Direct Summand Basis Theorem
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- 1.Donna Beers, R. Hunter, and E. Walker, Finite Valued p-Groups, Abelian Group Theory, Lecture Notes in Mathematics 1006, Springer-Verlag, New York 1983.Google Scholar
- 3.Laszlo Fuchs, Infinite. Abelian Groups, vol. 1, Academic Press New York and London, 1970.Google Scholar
- 4.S. A. Khabbaz and G. Rayna, A Basis Theorem for Subgroups of Finite Abelian Groups, Abelian Group Theory, Lecture Notes in Mathematics 1006, Springer-Verlag, New York 1983.Google Scholar