# On Rusakov’s $n$-ary $rs$-groups

Wiesław Aleksander Dudek; Zoran Stojaković

Czechoslovak Mathematical Journal (2001)

- Volume: 51, Issue: 2, page 275-283
- ISSN: 0011-4642

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topDudek, Wiesław Aleksander, and Stojaković, Zoran. "On Rusakov’s $n$-ary $rs$-groups." Czechoslovak Mathematical Journal 51.2 (2001): 275-283. <http://eudml.org/doc/30634>.

@article{Dudek2001,

abstract = {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.},

author = {Dudek, Wiesław Aleksander, Stojaković, Zoran},

journal = {Czechoslovak Mathematical Journal},

keywords = {$n$-ary group; symmetry; -ary groups; symmetries; -groups derived from binary groups},

language = {eng},

number = {2},

pages = {275-283},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {On Rusakov’s $n$-ary $rs$-groups},

url = {http://eudml.org/doc/30634},

volume = {51},

year = {2001},

}

TY - JOUR

AU - Dudek, Wiesław Aleksander

AU - Stojaković, Zoran

TI - On Rusakov’s $n$-ary $rs$-groups

JO - Czechoslovak Mathematical Journal

PY - 2001

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 51

IS - 2

SP - 275

EP - 283

AB - 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.

LA - eng

KW - $n$-ary group; symmetry; -ary groups; symmetries; -groups derived from binary groups

UR - http://eudml.org/doc/30634

ER -

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