Note on elongations of totally projective p-groups by p ω+n -projective p-groups

Danchev, Peter V.

doi:10.1007/s10986-006-0017-z

Cited by 3 publications

(1 citation statement)

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“…Consequently, owing to (1), p 2 T = 0 and again with the help of the aforementioned Nunke's criterion we deduce that A is p !+2 -projective. The fact that A is not p !+1 -projective follows in accordance with our result established in [7] or [8], which says that every p !+1 -projective summable group must be a direct sum of countable groups, combined with the alluded to above property (3).…”

Section: Examplesupporting

confidence: 89%

Nice bases for primary Abelian groups

Danchev¹

2007

Ann. Univ. Ferrara

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Suppose that A is an Abelian p-group. It is proved that if p ! A is bounded, then A has a bounded nice basis and if p ! A is a direct sum of cyclic groups, then A has a nice basis. In particular, all Abelian p-groups of length < !.2 along with all simply presented Abelian p-groups are equipped with bounded nice bases. It is also shown that if length(A) ≤ !.2 and A/p ! A is countable, then A possesses a bounded nice basis as well as if length(A) ≤ !.2 and p ! A is countable, then A possesses a nice basis. Moreover, contrasting with these claims, we demonstrate that if length(A) = !.2 and A/p ! A is torsion-complete with finite Ulm-Kaplansky invariants, then A does not have a bounded nice basis. If in addition p ! A is torsion-complete, then A does not have a nice basis, respectively. Finally, we construct a summable p !+2 -projective group (thus a summable group with a nice basis) which is not a direct sum of countable groups. This answers in negative our question posed in (Atti Sem. Mat. Fis. Univ. Modena e Reggio Emilia, 2005).

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Section: Examplesupporting

confidence: 89%