Planar varieties of semigroups

D. V. Solomatin

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 232-247.

Résumé

We study the property of planarity of Cayley graphs for varieties of semigroups. It is proved that the variety of semigroups with zero multiplication $\mathrm{ var}\{xy=zt\}$, the variety of left zero semigroups $\mathrm{ var}\{xy=x\}$ and the variety $\mathrm{ var}\{xy=xz\}$ are the only non-trivial planar variety of semigroups. We find the ranks of planarity for some important series of varieties of semigroups.

Détail

Keywords: semigroup, Cayley graph, variety of semigroups, planar graph, rank of planarity.

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