Geodesic
UNCOUNTABLY MANY VARIETIES OF COMPLETELY SIMPLE SEMIGROUPS WITH METABELIAN SUBGROUPS
Glasgow mathematical journal, Tome 48 (2006) no. 3, pp. 365-410

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DOI

It has been proved by D. E. Cohen [1] that the lattice of all varieties of metabelian groups is countable. In this paper, we show that the lattice of all varieties of completely simple semigroups with metabelian subgroups has the cardinality of the continuum. M. Petrich and N. R. Reilly have introduced in [6] the notion of near varieties of idempotent generated completely simple semigroups. The mapping assigning to every variety $\mathcal{V}$ of completely simple semigroups the class of all idempotent generated members of $\mathcal{V}$ is a complete lattice homomorphism of the lattice of all varieties of completely simple semigroups onto the lattice of all near varieties of idempotent generated completely simple semigroups. In this paper we show that, in fact, the lattice of all near varieties of idempotent generated completely simple semigroups with metabelian subgroups has itself the cardinality of the continuum.
DOI : 10.1017/S0017089506003132
Mots-clés : Primary 20M07, Secondary 20E10 
KAĎOUREK, JIŘÍ. UNCOUNTABLY MANY VARIETIES OF COMPLETELY SIMPLE SEMIGROUPS WITH METABELIAN SUBGROUPS. Glasgow mathematical journal, Tome 48 (2006) no. 3, pp. 365-410. doi: 10.1017/S0017089506003132
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     author = {KA\v{D}OUREK, JI\v{R}\'I},
     title = {UNCOUNTABLY {MANY} {VARIETIES} {OF} {COMPLETELY} {SIMPLE} {SEMIGROUPS} {WITH} {METABELIAN} {SUBGROUPS}},
     journal = {Glasgow mathematical journal},
     pages = {365--410},
     year = {2006},
     volume = {48},
     number = {3},
     doi = {10.1017/S0017089506003132},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089506003132/}
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