On a probabilistic problem on finite semigroups

Attila Nagy; Csaba Tóth

Commentationes Mathematicae Universitatis Carolinae (2023)

  • Volume: 64, Issue: 4, page 395-410
  • ISSN: 0010-2628

Abstract

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We deal with the following problem: how does the structure of a finite semigroup S depend on the probability that two elements selected at random from S , with replacement, define the same inner right translation of S . We solve a subcase of this problem. As the main result of the paper, we show how to construct not necessarily finite medial semigroups in which the index of the kernel of the right regular representation equals two.

How to cite

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Nagy, Attila, and Tóth, Csaba. "On a probabilistic problem on finite semigroups." Commentationes Mathematicae Universitatis Carolinae 64.4 (2023): 395-410. <http://eudml.org/doc/299326>.

@article{Nagy2023,
abstract = {We deal with the following problem: how does the structure of a finite semigroup $S$ depend on the probability that two elements selected at random from $S$, with replacement, define the same inner right translation of $S$. We solve a subcase of this problem. As the main result of the paper, we show how to construct not necessarily finite medial semigroups in which the index of the kernel of the right regular representation equals two.},
author = {Nagy, Attila, Tóth, Csaba},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {semigroup; regular representation of semigroups; medial semigroup},
language = {eng},
number = {4},
pages = {395-410},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On a probabilistic problem on finite semigroups},
url = {http://eudml.org/doc/299326},
volume = {64},
year = {2023},
}

TY - JOUR
AU - Nagy, Attila
AU - Tóth, Csaba
TI - On a probabilistic problem on finite semigroups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2023
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 64
IS - 4
SP - 395
EP - 410
AB - We deal with the following problem: how does the structure of a finite semigroup $S$ depend on the probability that two elements selected at random from $S$, with replacement, define the same inner right translation of $S$. We solve a subcase of this problem. As the main result of the paper, we show how to construct not necessarily finite medial semigroups in which the index of the kernel of the right regular representation equals two.
LA - eng
KW - semigroup; regular representation of semigroups; medial semigroup
UR - http://eudml.org/doc/299326
ER -

References

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