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Complexite des demi — Groupes de matrices

  • G. Jacob
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 52)

Abstract

Let us call measure of complexity over a class ℋ of semigroups any function β from IN into IN such that any semigroup H in ℋ generated by at most n elements has its cardinality less than β(n). If β is a measure of complexity over the class of all subgroups of a finite matrix semigroup H, then we can compute an integer T(β) which is greater than the cardinality of H. We give here equations computing effectively such an integer T(β) for some classes of matrix semigroups, or of quotients semigroups of matrix semigroups.

As a consequence we prove, using a theorem of A.I. Kostrikin, that there exist an effective decision procedure for the finiteness of matrix semigroups over skewfields, under the condition that each of its elements admits a given prime integer p as period.

Keywords

Strictement Positif Quotient Semigroup Nous Donnons Nous Rappelons Dimension Finie 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  • G. Jacob
    • 1
  1. 1.Université Lille I et Laboratoire d'Informatique Théorique et Programmation (C.N.R.S., laboratoire associé 248)France

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