John D. Dixon

Exact solution of linear equations usingP-adic expansions

SummaryA method is described for computing the exact rational solution to a regular systemAx=b of linear equations with integer coefficients. The method involves: (i) computing the inverse (modp) ofA for some primep; (ii) using successive refinements to compute an integer vector

The primitive permutation groups of degree less than 1000

\bar x

Random sets which invariably generate the symmetric group

such that

Profinite completions and isomorphic finite quotients

A\bar x \equiv b

An isomorphism criterion for modules over a principal ideal domain

(modpm) for a suitably large integerm; and (iii) deducing the rational solutionx from thep-adic approximation