TY - JOUR
T1 - On reconstructing separable reduced p-groups with a given socle
AU - Shelah, Saharon
PY - 1987/6
Y1 - 1987/6
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=51249172760&partnerID=8YFLogxK
U2 - 10.1007/BF02790788
DO - 10.1007/BF02790788
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AN - SCOPUS:51249172760
SN - 0021-2172
VL - 60
SP - 146
EP - 166
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 2
ER -