| Title:
|
On the maximal subgroup of the sandwich semigroup of generalized circulant Boolean matrices (English) |
| Author:
|
Chen, Jinsong |
| Author:
|
Tan, Yijia |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
4 |
| Year:
|
2006 |
| Pages:
|
1117-1129 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
generalized ciculant Boolean matrix |
| Keyword:
|
sandwich semigroup |
| Keyword:
|
idempotent element |
| Keyword:
|
maximal subgroup |
| MSC:
|
06F30 |
| MSC:
|
15A33 |
| MSC:
|
15A36 |
| idZBL:
|
Zbl 1164.15323 |
| idMR:
|
MR2280798 |
| . |
| Date available:
|
2009-09-24T11:41:35Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128134 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| . |
