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http://dx.doi.org/10.4134/CKMS.c190013

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)
Publication Information
Communications of the Korean Mathematical Society / v.35, no.1, 2020 , pp. 83-116 More about this Journal
Abstract
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.
Keywords
Product-one sequences; Davenport constant; dihedral groups; dicyclic groups; sets of lengths; unions of sets of lengths;
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