On skew elements in polyadic groups of special form

A. M. Gal'mak

Problemy fiziki, matematiki i tehniki, no. 2 (2020), pp. 64-68

Résumé

The article goes on with a study of skew elements in polyadic groups of special form, that is in polyadic groups with $l$-ary operation $\eta_{s,\sigma,k}$, that is called polyadic operation of special form and is defined on Cartesian power of $A^k$ $n$-ary group $\langle A,\eta\rangle$ by substitution $\sigma\in\mathbf{S}_k$ which order divides $l-1$ and $n$-ary operation $\eta$. In particular a theorem has been proved that allows us to determine a skew element for each element of $l$-ary group of a special form, the skew element being formulated by means of a inverse sequences of $n$-ary group on Cartesian power of which the given $l$-ary group is constructed.

Détail

Keywords: polyadic operation, $n$-ary group, skew element, inverse sequence.