On product-one sequences over dihedral groups

@article{Geroldinger2020OnPS,
  title={On product-one sequences over dihedral groups},
  author={Alfred Geroldinger and David J. Grynkiewicz and Jun Seok Oh and Qinghai Zhong},
  journal={Journal of Algebra and Its Applications},
  year={2020}
}
Let [Formula: see text] be a finite group. A sequence over [Formula: see text] means a finite sequence of terms from [Formula: see text], where repetition is allowed and the order is disregarded. A product-one sequence is a sequence whose elements can be ordered such that their product equals the identity element of the group. The set of all product-one sequences over [Formula: see text] (with the concatenation of sequences as the operation) is a finitely generated C-monoid. Product-one… Expand
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References

SHOWING 1-10 OF 57 REFERENCES
On minimal product-one sequences of maximal length over Dihedral and Dicyclic groups
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 beExpand
On the algebraic and arithmetic structure of the monoid of product-one sequences II
  • J. Oh
  • Computer Science, Mathematics
  • Period. Math. Hung.
  • 2019
TLDR
The present paper shows that the class semigroup is Clifford (i.e., a union of groups) if and only if $$|G'| \le 2$$|G′|≤2 if andonly if $${\mathcal {B}} (G)$$B(G) is seminormal. Expand
The large Davenport constant I: Groups with a cyclic, index 2 subgroup
Let G be a finite group written multiplicatively. By a sequence over G, we mean a finite sequence of terms from G which is unordered, repetition of terms allowed, and we say that it is a product-oneExpand
Extremal product-one free sequences in Dihedral and Dicyclic Groups
TLDR
This paper gives explicit characterizations of all sequences S of G such that | S | = D ( G ) − 1 and S is free of subsequences whose product is 1, where G is equal to D 2 n or Q 4 n for some n. Expand
The Large Davenport Constant II: General Upper Bounds
Let $G$ be a finite group written multiplicatively. By a sequence over $G$, we mean a finite sequence of terms from $G$ which is unordered, repetition of terms allowed, and we say that it is aExpand
The Interplay of Invariant Theory with Multiplicative Ideal Theory and with Arithmetic Combinatorics
This paper surveys and develops links between polynomial invariants of finite groups, factorization theory of Krull domains, and product-one sequences over finite groups. The goal is to gain a betterExpand
On congruence half-factorial Krull monoids with cyclic class group
We carry out a detailed investigation of congruence half-factorial Krull monoids with finite cyclic class group and related problems. Specifically, we determine precisely all relatively large valuesExpand
The Noether number of p-groups
  • K. Cziszter
  • Mathematics
  • Journal of Algebra and Its Applications
  • 2019
A group of order [Formula: see text] ([Formula: see text] prime) has an indecomposable polynomial invariant of degree at least [Formula: see text] if and only if the group has a cyclic subgroup ofExpand
Sets of minimal distances and characterizations of class groups of Krull monoids
Let H be a Krull monoid with finite class group G such that every class contains a prime divisor. Then every non-unit $$a \in H$$a∈H can be written as a finite product of atoms, say $$a=u_1 \cdotExpand
The Noether numbers and the Davenport constants of the groups of order less than 32
Abstract The computation of the Noether numbers of all groups of order less than thirty-two is completed. It turns out that for these groups in non-modular characteristic the Noether number isExpand
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