On the locality of the pseudovariety DG
| Authors | |
|---|---|
| Year of publication | 2008 |
| Type | Article in Periodical |
| Magazine / Source | Journal of the Institute of Mathematics of Jussieu |
| MU Faculty or unit | |
| Citation | |
| Web | Cambridge Journals Online - Journal of the Institute of Mathematics of Jussieu |
| Field | General mathematics |
| Keywords | pseudovarieties of finite monoids and finite categories; locally finite varieties of monoids and categories; finitely generated relatively free monoids and categories; Mal'cev products of locally finite varieties of groups |
| Description | The pseudovariety DG of all finite monoids all of whose regular D-classes are subgroups is shown to be local, that is, it is verified that the pseudovariety gDG of finite categories generated by DG coincides with the pseudovariety lDG of all finite categories whose local monoids all belong to DG. Yet more general statements of this kind are deduced, yielding results such as that, for every prime number p, the pseudovariety DGp of all finite monoids all of whose regular D-classes are p-groups is local, or that the pseudovarieties DGsol and DGnil of all finite monoids all of whose regular D-classes are, respectively, solvable groups and nilpotent groups are local. |
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