Central Operation of the (n,m)-Group

Radoslav Galić ; Anita Katić

Mathematica Moravica, Tome 14 (2010) no. 1.

Résumé

In this paper we have defined a central operation of the (n,m)-group, as a mapping $\alpha$ of the set $Q^{n-2m}$ into the set $Q^{m}$, such that for every $a_{1}^{n-2m}, b_{1}^{n-2m}\in Q$ and for every $x_{1}^{m}\in Q^{m}$ the following equality holds: $A(\alpha(a_{1}^{n-2m}), a_{1}^{n-2m}, x_{1}^{m}) = A(x_{1}^{m}, \alpha(b_{1}^{n-2m}), b_{1}^{n-2m})$. This is a generalization of the notion of a central operation of the n-group, i.e. of the central element of a binary group. The notion of the central operation of the n-group was defined by Janez Ušan in [4]. Furthermore, in this paper we have proved some claims which hold for the central operation of the (n, m)-group.

Détail

Mots-clés : (n;m)-group, {1, n − m + 1}-neutral operation, inverse operation of the (n;m)-groupoid, central operation