Uncountably many varieties of completely simple semigroups with metabelian subgroups
| Authors | |
|---|---|
| Year of publication | 2006 |
| Type | Article in Periodical |
| Magazine / Source | Glasgow Mathematical Journal |
| MU Faculty or unit | |
| Citation | |
| Field | General mathematics |
| Keywords | variety of completely simple semigroups; metabelian group |
| Description | It has been proved by D. E. Cohen in 1967 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 a paper of 1983 the notion of near varieties of idempotent generated completely simple semigroups. The mapping assigning to every variety V of completely simple semigroups the class of all idempotent generated members of 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. |
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