On skew elements in polyadic groups of special form defined by cyclic substitution

A. M. Gal'mak

Problemy fiziki, matematiki i tehniki, no. 3 (2020), pp. 55-60

Résumé

The article goes on with a study of skew elements in polyadic groups of special form defined by cyclic substitution, 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 $A^k$ of $n$-ary group $\langle A,\eta\rangle$ by cyclic substitution $\sigma\in\mathbf{S}_k$ satisfying the condition $\sigma^l=\sigma$, and $n$-ary operation $\eta$. As corollaries the results for polyadic groups were obtained. These polyadic groups are of special form with $l$-ary operation $\eta_{s,\sigma,k}$ in which $\sigma$ is a cycle such that its length devides $l-1$, in particular, $\sigma$ may be cycle of the form $(12\dots k)$.

Détail

Keywords: polyadic operation, $n$-ary group, skew element
Mots-clés : substitution.