Abstract
We consider the following question: When do two finite abelian groups have isomorphic lattices of characteristic subgroups? An explicit description of the characteristic subgroups of such groups enables us to give a complete answer to this question, in the case where at least one of the groups has odd order. An “exceptional” isomorphism, which occurs between the lattice of characteristic subgroups of Z p × Z p 2 × Z p 4 and Z p 2 × Z p 5 , for any prime p, is noteworthy.
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