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An automata-theoretic approach to the study of the intersection of two submonoids of a free monoid

Laura Giambruno, Antonio Restivo (2008)

RAIRO - Theoretical Informatics and Applications

We investigate the intersection of two finitely generated submonoids of the free monoid on a finite alphabet. To this purpose, we consider automata that recognize such submonoids and we study the product automata recognizing their intersection. By using automata methods we obtain a new proof of a result of Karhumäki on the characterization of the intersection of two submonoids of rank two, in the case of prefix (or suffix) generators. In a more general setting, for an arbitrary number of generators,...

An autostable 2 nilpotent group with no Scott family of finitary formulas.

Tusupov, D.A. (2007)

Sibirskij Matematicheskij Zhurnal

An axiomatic approach for the Hajós theorem.

Corrádi, Keresztély, Szabó, Sándor (1997)

Beiträge zur Algebra und Geometrie

An easy proof of Ponizovski's theorem.

M. Gould (1977/1978)

Semigroup forum

An elementary approach to the mapping class group of a surface.

Wajnryb, Bronislaw (1999)

Geometry & Topology

An elementary class extending abelian-by- $G$ groups, for $G$ infinite

Carlo Toffalori (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We show that for no infinite group $G$ the class of abelian-by- $G$ groups is elementary, but, at least when $G$ is an infinite elementary abelian $p$ -group (with $p$ prime), the class of groups admitting a normal abelian subgroup whose quotient group is elementarily equivalent to $G$ is elementary.