• 제목/요약/키워드: Davenport constant

검색결과 1건 처리시간 0.014초

ON MINIMAL PRODUCT-ONE SEQUENCES OF MAXIMAL LENGTH OVER DIHEDRAL AND DICYCLIC GROUPS

  • Oh, Jun Seok;Zhong, Qinghai
    • 대한수학회논문집
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    • 제35권1호
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    • pp.83-116
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    • 2020
  • 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 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 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.