On Countable Extensions of Primary Abelian Groups
نویسندگان
چکیده
It is proved that if A is an abelian p-group with a pure subgroup G so that A/G is at most countable and G is either p-totally projective or p-summable, then A is either p-totally projective or p-summable as well. Moreover, if in addition G is nice in A, then G being either strongly p-totally projective or strongly p-summable implies that so is A. This generalizes a classical result of Wallace (J. Algebra, 1971) for totally projective p-groups as well as continues our recent investigations in (Arch. Math. (Brno), 2005 and 2006). Some other related results are also established.
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