Chains and anti-chains in the lattice of epigroup varieties

Details Chains and anti-chains in the lattice of epigroup varieties Chains and anti-chains in the lattice of epigroup varieties

2009-11-16

arxiv.org/abs/0911.2743v1

Mathematics

Group Theory

5 pages, 2 figures

Scientific paper

Let $\mathcal E_n$ be the variety of all epigroups of index $\le n$. We prove
that, for an arbitrary natural number $n$, the interval $[\mathcal E_n,
\mathcal E_{n+1}]$ of the lattice of epigroup varieties contains a chain
isomorphic to the chain of real numbers with the usual order and an anti-chain
of the cardinality continuum.

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