| Title:
|
On congruence permutable $G$-sets (English) |
| Author:
|
Nagy, Attila |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
61 |
| Issue:
|
2 |
| Year:
|
2020 |
| Pages:
|
139-145 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
An algebraic structure is said to be congruence permutable if its arbitrary congruences $\alpha$ and $\beta$ satisfy the equation $\alpha \circ \beta =\beta \circ \alpha$, where $\circ$ denotes the usual composition of binary relations. To an arbitrary $G$-set $X$ satisfying $G\cap X=\emptyset$, we assign a semigroup $(G,X,0)$ on the base set $G\cup X\cup \{ 0\}$ containing a zero element $0\notin G\cup X$, and examine the connection between the congruence permutability of the $G$-set $X$ and the semigroup $(G,X,0)$. (English) |
| Keyword:
|
$G$-set |
| Keyword:
|
congruence permutable algebras |
| Keyword:
|
semigroup |
| MSC:
|
20E15 |
| MSC:
|
20M05 |
| idZBL:
|
Zbl 07285996 |
| idMR:
|
MR4143700 |
| DOI:
|
10.14712/1213-7243.2020.019 |
| . |
| Date available:
|
2020-10-13T13:05:58Z |
| Last updated:
|
2022-07-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148288 |
| . |
| Reference:
|
[1] Clifford A. H., Preston G. B.: The Algebraic Theory of Semigroups, Vol. I.Mathematical Surveys, No. 7, American Mathematical Society, Providence, 1961. MR 0132791 |
| Reference:
|
[2] Deák A., Nagy A.: Finite permutable Putcha semigroups.Acta Sci. Math. (Szeged) 76 (2010), no. 3–4, 397–410. MR 2789677 |
| Reference:
|
[3] Hamilton H.: Permutability of congruences on commutative semigroups.Semigroup Forum 10 (1975/76), no. 1, 55–66. MR 0387455, 10.1007/BF02194872 |
| Reference:
|
[4] McKenzien R. N., McNulty G. F., Taylor W. F.: Algebras, Lattices, Varieties, Vol. I.The Wadsworth & Brooks/Cole Mathematics Series, Wadsworth & Brooks/Cole Advanced Books & Software, Monterey, CA, 1987. MR 0883644 |
| Reference:
|
[5] Nagy A.: Special Classes of Semigroups.Advances in Mathematics (Dordrecht), 1, Kluwer Academic Publishers, Dordrecht, 2001. MR 1777265 |
| Reference:
|
[6] Pálfy P. P., Pudlák P.: Congruence lattices of finite algebras and intervals in subgroup lattices of finite groups.Algebra Universalis 11 (1980), no. 1, 22–27. MR 0593011, 10.1007/BF02483080 |
| Reference:
|
[7] Pálfy P. P., Saxl J.: Congruence lattices of finite algebras and factorizations of groups.Comm. Algebra 18 (1990), no. 9, 2783–2790. MR 1063342, 10.1080/00927879008824052 |
| Reference:
|
[8] Vernikov B. M.: On congruences of $G$-sets.Comment. Math. Univ. Carolin. 38 (1997), no. 3, 601–611. MR 1485081 |
| . |
