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Adolfo Ballester-Bolinches, Jean-Éric Pin, Xaro Soler-Escrivà
Languages associated with saturated formations of groups
Forum Math., 27(3) (2015), 1471–1505
http://dx.doi.org/10.1515/forum-2012-0161
Abstract
In a previous paper, the authors have shown that Eilenberg’s variety theorem can be extended to more general structures, called formations. In this paper, we give a general method to describe the languages corresponding to saturated formations of groups, which are widely studied in group theory. We recover in this way a number of known results about the languages corresponding to the classes of nilpotent groups, soluble groups and supersoluble groups. Our method also applies to new examples, like the class of groups having a Sylow tower.
2010 Mathematics subject classification: 68Q70; 20D10
Keywords: Group formation; regular language; finite automata; finite monoid