One Characterization of Near-P-Polyagroup

Janez Ušan

Mathematica Moravica, Tome 6 (2002) no. 1.

Résumé

In the present paper the following proposition is proved. Let $k>l$, $s>1$, $n = k \cdot s + 1$ and let $(Q, A)$ be an n-groupoid. Then, $(Q, A)$ is an near-P-polyagroup (briefly: NP-polyagroup) of the type $(s,n-1)$ iff for some $i\in\bigl\{t\cdot s+l\mid t\in\{1,\dots,k-1\}\bigr\}$ the following conditions hold: (a) the $\langle i-s, i\rangle$ - associative law holds in $(Q, A)$; (b) the $\langle i,i+s\rangle$ - associative law holds in $(Q, A)$; and (c) for every $a_{1}^{n}\in Q$ there is exactly one $x\in Q$ such that the following equality holds $A(a_{1}^{i-1},x,a_{i}^{n-1}) = a_{n}$.

Détail

Mots-clés : n-groupoid;n-semigroup, n-quasigroup, Ps-associative n-groupoid, P-polyagroup, NP-polyagroup