대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제35권1호
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  • Pages.83-116
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  • 2020
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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ON MINIMAL PRODUCT-ONE SEQUENCES OF MAXIMAL LENGTH OVER DIHEDRAL AND DICYCLIC GROUPS

  • Oh, Jun Seok (Institute for Mathematics and Scientific Computing University of Graz) ;
  • Zhong, Qinghai (Institute for Mathematics and Scientific Computing University of Graz)
  • 투고 : 2019.01.13
  • 심사 : 2019.05.02
  • 발행 : 2020.01.31
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초록

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.

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과제정보

This work was supported by the Austrian Science Fund FWF, W1230 Doctoral Program Discrete Mathematics and Project No. P28864–N35.

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