1. On Rusakov’s $n$-ary $rs$-groups.
- Creator:
- Dudek, Wiesław Aleksander and Stojaković, Zoran
- Type:
- model:article and TEXT
- Subject:
- $n$-ary group and symmetry
- Language:
- English
- Description:
- Properties of $n$-ary groups connected with the affine geometry are considered. Some conditions for an $n$-ary $rs$-group to be derived from a binary group are given. Necessary and sufficient conditions for an $n$-ary group $<\theta ,b>$-derived from an additive group of a field to be an $rs$-group are obtained. The existence of non-commutative $n$-ary $rs$-groups which are not derived from any group of arity $m<n$ for every $n\ge 3$, $r>2$ is proved.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public