Let $A, B$ be isomorphic finite abelian groups and $T\subseteq A$ a subgroup. Let $i:T \to B$ be a monomorphism. Is there an isomorphism $f:A \to B$, s.t. $f|_T=i$? If not, is there a condition for such a map to exist?
2026-03-24 23:44:18.1774395858
Extension of map between finite abelian groups
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Not always. For example in the direct product of Z4 and Z2 there are two gruops of order 2 one is Z2 and the other is subgruop of Z4. This two groups externaly are the isomorphic but there are included in the product different. One is Subgruop of a group of order 4 and the other not.
https://groupprops.subwiki.org/wiki/Subgroup_structure_of_direct_product_of_Z4_and_Z2