### Chains and anti-chains in the lattice of epigroup varietiesChains and anti-chains in the lattice of epigroup varieties

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 Author Skokov, D. V. ♦ Vernikov, B. M. Source arXiv.org Content type Text File Format PDF Date of Submission 2009-11-16 Language English
 Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics Subject Keyword Mathematics - Group Theory ♦ 20M07 ♦ 08B15 ♦ math Abstract 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. Educational Use Research Learning Resource Type Article Page Count 5