The consecutive Davenport constant conjecture for finite groups

Let GG be a finite group, and let C(G){\sf C}(G) denote its consecutive Davenport constant, namely the least length \ell such that every sequence of ellell elements of GG contains a nonempty consecutive product-one subsequence.

Consecutive Davenport constant conjecture. For every finite group GG, it holds

C(G)=G.{\sf C}(G)=|G|.

The equality is established in the source for finite abelian groups and metacyclic groups, as well as for direct products of a finite abelian group with a metacyclic group. The general case remains open.

Sources & referencesView supporting material

Primary source

A. Lemos, A. O. Moura, S. Ribas and A. T. Silva, “A note on weighted consecutive Davenport constant”, arXiv:2404.11312 (2024).

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