Davenport constant for $C_n^3$

Upper bound, last-listed row

| $4$ | [Grinsztajn2026] | From the pointwise estimate $D(C_n^3)\le 4n-P(n)-2$, where $P(n)=\max_{p^a\parallel n}p^a$. Since $P(n)\ge2$, this gives $C_{53}\le4$. |

exact pinned row

| $4$ | <a href="#Grinsztajn2026">[Grinsztajn2026]</a> | From the pointwise estimate $D(C_n^3)\le 4n-P(n)-2$, where $P(n)=\max_{p^a\parallel n}p^a$. Since $P(n)\ge2$, this gives $C_{53}\le4$. |

value changed 2026-09-05

Lower bound, last-listed row

| $3$ | [GG2006] | Using $d(C_n^3)\ge d^\*(C_n^3)=3(n-1)$ and $D(G)=1+d(G)$ gives $D(C_n^3)\ge 3(n-1)+1$, hence $C_{53}\ge 3$. [GG2006-d-ge-dstar] [GG2006-D-equals-1-plus-d] [GG2006-def-dstar] |

exact pinned row

| $3$ | <a href="#GG2006">[GG2006]</a> | Using $d(C_n^3)\ge d^\*(C_n^3)=3(n-1)$ and $D(G)=1+d(G)$ gives $D(C_n^3)\ge 3(n-1)+1$, hence $C_{53}\ge 3$. <a href="#GG2006-d-ge-dstar">[GG2006-d-ge-dstar]</a> <a href="#GG2006-D-equals-1-plus-d">[GG2006-D-equals-1-plus-d]</a> <a href="#GG2006-def-dstar">[GG2006-def-dstar]</a> |

text edited 2026-08-24 — bound unchanged