Search results for " 20D10"
showing 3 items of 3 documents
Languages associated with saturated formations of groups
2013
International audience; 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.; Dans un article précédent, les auteurs avaient montré comment étendre le théorème des variétés d'Eilenberg à des structures plus g…
Formations of finite monoids and formal languages: Eilenberg’s variety theorem revisited
2014
International audience; We present an extension of Eilenberg's variety theorem, a well-known result connecting algebra to formal languages. We prove that there is a bijective correspondence between formations of finite monoids and certain classes of languages, the formations of languages. Our result permits to treat classes of finite monoids which are not necessarily closed under taking submonoids, contrary to the original theory. We also prove a similar result for ordered monoids.; Nous présentons une extension du théorème des variétés d'Eilenberg, un résultat célèbre reliant l'algèbre à la théorie des langages formels. Nous montrons qu'il existe une correspondance bijective entre les form…
On the Frattini subgroup of a finite group
2016
We study the class of finite groups $G$ satisfying $\Phi (G/N)= \Phi(G)N/N$ for all normal subgroups $N$ of $G$. As a consequence of our main results we extend and amplify a theorem of Doerk concerning this class from the soluble universe to all finite groups and answer in the affirmative a long-standing question of Christensen whether the class of finite groups which possess complements for each of their normal subgroups is subnormally closed.