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{\bf Wolfgang A. Schmid}
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{\bf The Inverse Problem Associated to the Davenport Constant for $C_2\oplus C_2 \oplus C_{2n}$, and Applications to the Arithmetical Characterization of Class Groups}
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The inverse problem associated to the Davenport constant for some
finite abelian group is the problem of determining the structure of
all minimal zero-sum sequences of maximal length over this group, and
more generally of long minimal zero-sum sequences. Results on the
maximal multiplicity of an element in a long minimal zero-sum sequence
for groups with large exponent are obtained. For groups of the form
$C_2^{r-1}\oplus C_{2n}$ the results are optimal up to an absolute
constant. And, the inverse problem, for sequences of maximal length,
is solved completely for groups of the form $C_2^2 \oplus C_{2n}$.
Some applications of this latter result are presented. In particular,
a characterization, via the system of sets of lengths, of the class
group of rings of algebraic integers is obtained for certain types of
groups, including $C_2^2 \oplus C_{2n}$ and $C_3 \oplus C_{3n}$; and
the Davenport constants of groups of the form $C_4^2 \oplus C_{4n}$
and $C_6^2 \oplus C_{6n}$ are determined.
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