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Let $G$ be a finite group. By a sequence over $G$, we mean a finite unordered sequence of terms from $G$, where repetition is allowed, and we say that it is a product-one sequence if its terms can be ordered such that their product equals the identity element of $G$. The large Davenport constant $\mathsf D (G)$ is the maximal length of a minimal product-one sequence, that is, a product-one sequence which cannot be factored into two non-trivial product-one subsequences. We provide explicit characterizations of all minimal product-one sequences of length $\mathsf D (G)$ over dihedral and dicyclic groups. Based on these characterizations we study the unions of sets of lengths of the monoid of product-one sequences over these groups.
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참고문헌 (32)
참고문헌 신청
N. R. Baeth / 2018 / Arithmetical invariants of local quaternion orders / Acta Arith 186(2):143~177
F. E. Brochero Martinez / 2018 / Extremal product-one free sequences in dihedral and dicyclic groups / Discrete Math 341(2):570~578
F. E. Brochero Martinez / The (1, s}-weighted Davenport constant in Zn and an application in an inverse problem
F. Chen / 2014 / Long minimal zero-sum sequences in the groups Cr-1 2⊕C2k / Integers 14:A23~A51
K. Cziszter / 2019 / The Noether number of p-groups / J. Algebra Appl 18(4):1950066~1950079
F. E. Brochero Martinez / 2018 / Extremal product-one free sequences in dihedral and dicyclic groups / Discrete Math 341(2):570~578
F. E. Brochero Martinez / The (1, s}-weighted Davenport constant in Zn and an application in an inverse problem
F. Chen / 2014 / Long minimal zero-sum sequences in the groups Cr-1 2⊕C2k / Integers 14:A23~A51
K. Cziszter / 2019 / The Noether number of p-groups / J. Algebra Appl 18(4):1950066~1950079
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