Geodesic
On a probabilistic problem on finite semigroups
Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 4, pp. 395-410
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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.
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.
DOI : 10.14712/1213-7243.2024.006
Classification : 20M10, 20M15
Keywords: semigroup; regular representation of semigroups; medial semigroup 
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Nagy, Attila; Tóth, Csaba. On a probabilistic problem on finite semigroups. Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 4, pp. 395-410. doi: 10.14712/1213-7243.2024.006

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