Premium Finiteness Conditions on Subgroups and Formal Language TheoryPremium
Author(s)
Frougny Christiane,
Sakarovitch Jacques,
Schupp Paul
Publication year1989
Publication title
proceedings of the london mathematical society
Resource typeJournals
We show in this article that the most usual finiteness conditions on a subgroup of a finitely generated group all have equivalent formulations in terms of formal language theory. This correspondence gives simple proofs of various theorems concerning intersections of subgroups and the preservation of finiteness conditions in a uniform manner. We then establish easily the theorems of Greibach and of Griffiths by considering free reductions of languages that describe the computations of pushdown automata in one case and of Turing machines in the other, thus making clear that they are essentially the same.
Subject(s)formal group , linguistics , mathematics , philosophy , pure mathematics
Language(s)English
SCImago Journal Rank1.899
H-Index65
eISSN1460-244X
pISSN0024-6115
DOI10.1112/plms/s3-58.1.74
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