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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 27, Issue 3


Languages associated with saturated formations of groups

Adolfo Ballester-Bolinches / Jean-Éric Pin / Xaro Soler-Escrivà
  • Departament d'Estadística i Investigació Operativa, Universitat d'Alacant, Sant Vicent del Raspeig, Ap. Correus 99, 03080 Alacant, Spain
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Published Online: 2013-04-09 | DOI: https://doi.org/10.1515/forum-2012-0161


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.

Keywords: Group formation; regular language; finite automata; finite monoid

MSC: 68Q70; 20D10

About the article

Received: 2012-11-06

Revised: 2013-01-22

Published Online: 2013-04-09

Published in Print: 2015-05-01

Funding Source: MICINN (Spain)

Award identifier / Grant number: MTM2010-19938-C03-01

Funding Source: MEC

Funding Source: ANR

Award identifier / Grant number: 2010 BLAN 0202 02 FREC

Funding Source: Universitat Politècnica de València

Award identifier / Grant number: PAID-02-09

Citation Information: Forum Mathematicum, Volume 27, Issue 3, Pages 1471–1505, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2012-0161.

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