On Rusakov’s n -ary r s -groups

Wiesław Aleksander Dudek; Zoran Stojaković

Czechoslovak Mathematical Journal (2001)

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

Abstract

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Properties of n -ary groups connected with the affine geometry are considered. Some conditions for an n -ary r s -group to be derived from a binary group are given. Necessary and sufficient conditions for an n -ary group < θ , b > -derived from an additive group of a field to be an r s -group are obtained. The existence of non-commutative n -ary r s -groups which are not derived from any group of arity m < n for every n ≥ 3 , r > 2 is proved.

How to cite

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Dudek, 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 -

References

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