Linking numbers, quandles and groups

We introduce a quandle invariant of classical and virtual links, denoted $Q_{tc} (L)$. This has the property that (L) \cong Q_{tc} (L')$ if only components $L$ $L'$ can be indexed in such way $L=K_1 \cup \dots K_{\mu}$, $L'=K'_1 K'_{\mu}$ for each index $i$, there is multiplier $\epsilon_i \in \{-1,1\}$ connects linking numbers over $K_i$ to $K'_i$ $L'$: $\ell_{j/i}(K_i,K_j)= \epsilon_i \ell_{j/i}(K'_i,K'_j)$ all $j \neq i$. also extend links theorem Chen, which relates nilpotent quotient $G(L)/G(L)_3$.