Automorphism group of the variant of the lattice of partitions of a finite set

Authors

  • O. G. Ganyushkin Taras Shevchenko National University of Kyiv
  • O. O. Desiateryk Taras Shevchenko National University of Kyiv

DOI:

https://doi.org/10.17721/1812-5409.2020/3.13

Abstract

In this paper we consider variants of the lattice of partitions of a finite set and study automorphism groups of this variants. We obtain irreducible generating sets for of the lattice of partitions of a finite set.

We prove that the automorphism group of the variant of the lattice of partitions of a finite set is a natural generalization of the wreath product. The first multiplier of this generalized wreath product is the direct product of the wreaths products, such that depends on the type of the variant generating partition and the second is defined by the certain set of symmetric groups.

Key words: semigroup, variant, lattice, automorphism group.

Pages of the article in the issue: 115 - 119

Language of the article: English

References

LYAPIN, E. (1960) Polugruppy. Moskva: Fizmatgiz.

CHASE, K. (1979) Sendwich semigroups of binary relations. Discrete Math. V. 28(3). p. 231-236.

HICKEY, J. (1983) Semigroups under a sendwich operation. Proc. Edinburg Math. Soc. (2). V. 26(3). p. 371-382.

KHAN, T. & LAWSON, M. (2001) Variants of regular semigroups. Semigroup Forum. V. 62(3). p. 358-374.

MAZORCHUK, V. & TSYAPUTA, G. (2008) Isolated subsemigroups in the variants of T_n Acta Math. Univ. Com. V. LXXVII, 1. p. 63-84.

GANYUSHKIN, O. & MAZORCHUK, V. (2009) Classical Finite Transformation Semirgoups. An Introduction. London: Springer–Verlag. Algebra and Applications.

DESIATERYK, O. (2015) Variants of commutative bands with zero. Bulletin of Taras Shevchenko National University of Kyiv, Series: Physics & Mathematics. V. 4. p. 15-20.

DESIATERYK, O. & GANYUSHKIN, O. (2018) Variants of a lattice of partitions of a countable set / Algebra and Discrete Mathematics. Vol 26. No 1. p. 8-18.

DOLINKA, I. & EAST, J. (2015) Variants of finite full transformation semigroups / Int. J. Algebra Comput. no. 8.25. p. 1187-1222.

No 3 (2020)

Downloads

How to Cite

Ganyushkin, O. G., & Desiateryk, O. O. (2020). Automorphism group of the variant of the lattice of partitions of a finite set. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (3), 115–119. https://doi.org/10.17721/1812-5409.2020/3.13

Issue

No. 3 (2020)

Section

Algebra, Geometry and Probability Theory

License

Authors who publish with this journal agree to the following terms:

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).