On reconstructing separable reduced p-groups with a given socle

Saharon Shelah*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

Let {Mathematical expression} be a separable reduced (abelian)p-group which is torsion complete. We ask whether for {Mathematical expression} there is {Mathematical expression}, H[p]=G[p], H not isomorphic to G. If G is the sum of cyclic groups or is torsion complete, the answer is easily no. For other G, we prove that the answer is yes assuming G.C.H. Even without G.C.H. the answer is yes if the density character of G is equal to Min n<ω|p nG|, i.e., {Mathematical expression} Of course, instead of two non-isomorphic we can get many, but we do not deal much with this.

Original languageEnglish
Pages (from-to)146-166
Number of pages21
JournalIsrael Journal of Mathematics
Volume60
Issue number2
DOIs
StatePublished - Jun 1987

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