Geodesic
Automorphism groups of superextensions of finite monogenic semigroups
Algebra and discrete mathematics, Tome 27 (2019) no. 2, pp. 165-190

Voir la notice de l'article provenant de la source Math-Net.Ru

A family $\mathcal L$ of subsets of a set $X$ is called linked if $A\cap B\ne\emptyset$ for any $A,B\in\mathcal L$. A linked family $\mathcal M$ of subsets of $X$ is maximal linked if $\mathcal M$ coincides with each linked family $\mathcal L$ on $X$ that contains $\mathcal M$. The superextension $\lambda(X)$ of $X$ consists of all maximal linked families on $X$. Any associative binary operation $*\colon X\times X \to X$ can be extended to an associative binary operation $*\colon \lambda(X)\times\lambda(X)\to\lambda(X)$. In the paper we study automorphisms of the superextensions of finite monogenic semigroups and characteristic ideals in such semigroups. In particular, we describe the automorphism groups of the superextensions of finite monogenic semigroups of cardinality $\leq 5$.
Keywords: monogenic semigroup, maximal linked upfamily, superextension
Mots-clés : automorphism group. 
@article{ADM_2019_27_2_a2,
     author = {Taras Banakh and Volodymyr Gavrylkiv},
     title = {Automorphism groups of  superextensions of finite monogenic semigroups},
     journal = {Algebra and discrete mathematics},
     pages = {165--190},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2019_27_2_a2/}
}
TY  - JOUR
AU  - Taras Banakh
AU  - Volodymyr Gavrylkiv
TI  - Automorphism groups of  superextensions of finite monogenic semigroups
JO  - Algebra and discrete mathematics
PY  - 2019
SP  - 165
EP  - 190
VL  - 27
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2019_27_2_a2/
LA  - en
ID  - ADM_2019_27_2_a2
ER  - 
%0 Journal Article
%A Taras Banakh
%A Volodymyr Gavrylkiv
%T Automorphism groups of  superextensions of finite monogenic semigroups
%J Algebra and discrete mathematics
%D 2019
%P 165-190
%V 27
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2019_27_2_a2/
%G en
%F ADM_2019_27_2_a2
Taras Banakh; Volodymyr Gavrylkiv. Automorphism groups of  superextensions of finite monogenic semigroups. Algebra and discrete mathematics, Tome 27 (2019) no. 2, pp. 165-190. http://geodesic.mathdoc.fr/item/ADM_2019_27_2_a2/