On the maximal subgroup of the sandwich semigroup of generalized circulant Boolean matrices

Chen, Jinsong, and Tan, Yi Jia. "On the maximal subgroup of the sandwich semigroup of generalized circulant Boolean matrices." Czechoslovak Mathematical Journal 56.4 (2006): 1117-1129. <http://eudml.org/doc/31094>.

@article{Chen2006,
abstract = {Let $n$ be a positive integer, and $C_\{n\} (r)$ the set of all $n\times n$$r$-circulant matrices over the Boolean algebra $B=\lbrace 0,1\rbrace $, $G_\{n\}=\bigcup _\{r=0\}^\{n-1\}C_\{n\}(r)$. For any fixed $r$-circulant matrix $C$ ($C\ne 0$) in $G_\{n\}$, we define an operation “$\ast $” in $G_\{n\}$ as follows: $A\ast B=ACB$ for any $A,B$ in $G_\{n\}$, where $ACB$ is the usual product of Boolean matrices. Then $(G_\{n\},\ast )$ is a semigroup. We denote this semigroup by $G_\{n\}(C)$ and call it the sandwich semigroup of generalized circulant Boolean matrices with sandwich matrix $C$. Let $F$ be an idempotent element in $G_\{n\}(C)$ and $M(F)$ the maximal subgroup in $G_\{n\}(C)$ containing the idempotent element $F$. In this paper, the elements in $M(F)$ are characterized and an algorithm to determine all the elements in $M(F)$ is given.},
author = {Chen, Jinsong, Tan, Yi Jia},
journal = {Czechoslovak Mathematical Journal},
keywords = {generalized ciculant Boolean matrix; sandwich semigroup; idempotent element; maximal subgroup; generalized circulant Boolean matrix; sandwich semigroup; idempotent element; maximal subgroup},
language = {eng},
number = {4},
pages = {1117-1129},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the maximal subgroup of the sandwich semigroup of generalized circulant Boolean matrices},
url = {http://eudml.org/doc/31094},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Chen, Jinsong
AU - Tan, Yi Jia
TI - On the maximal subgroup of the sandwich semigroup of generalized circulant Boolean matrices
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 4
SP - 1117
EP - 1129
AB - Let $n$ be a positive integer, and $C_{n} (r)$ the set of all $n\times n$$r$-circulant matrices over the Boolean algebra $B=\lbrace 0,1\rbrace $, $G_{n}=\bigcup _{r=0}^{n-1}C_{n}(r)$. For any fixed $r$-circulant matrix $C$ ($C\ne 0$) in $G_{n}$, we define an operation “$\ast $” in $G_{n}$ as follows: $A\ast B=ACB$ for any $A,B$ in $G_{n}$, where $ACB$ is the usual product of Boolean matrices. Then $(G_{n},\ast )$ is a semigroup. We denote this semigroup by $G_{n}(C)$ and call it the sandwich semigroup of generalized circulant Boolean matrices with sandwich matrix $C$. Let $F$ be an idempotent element in $G_{n}(C)$ and $M(F)$ the maximal subgroup in $G_{n}(C)$ containing the idempotent element $F$. In this paper, the elements in $M(F)$ are characterized and an algorithm to determine all the elements in $M(F)$ is given.
LA - eng
KW - generalized ciculant Boolean matrix; sandwich semigroup; idempotent element; maximal subgroup; generalized circulant Boolean matrix; sandwich semigroup; idempotent element; maximal subgroup
UR - http://eudml.org/doc/31094
ER -