John D. Dixon



Professor Emeritus in the School of Mathematics and Statistics, Carleton University
Ph.D. (McGill)

My research interests are in group theory and in design and analysis of algorithms in various areas of algebra and related fields, but I am also interested in other areas of mathematics. I have written five books (some with co-authors) and about 75 papers; some of these publications are listed below. I have been retired since 2002.

Selected Publications

John D. Dixon and Irwin S. Pressman, Generalized commutators and a problem related to the Amitsur-Levitzki theorem (to appear in Linear and Multilinear Algebra) (pdf file 144 kb)

John D. Dixon, Recognizing cyclic matrices and a conjecture of J.G. Thompson, arXiv (

John D. Dixon, Longest common subsequences in binary sequences, arXiv (

Yuly Billig and John D. Dixon, An eigenvalue theorem for systems of polynomial equations, Amer. Math. Monthly 121 (2014) 150-153 (pdf file 101 kb)

Vahid Dabbaghian and John D. Dixon, Computing characters of groups with central subgroups, LCM J. Comput. and Math. 16 (2013) 398-406 ( pdf file 386 kb)

Vahid Dabbaghian and John D. Dixon, Computing matrix representations, Math. Comp. 79 (2010) 1801-1810 (pdf file 165 kb)

John D. Dixon,
Generating random elements in finite groups,  Electronic J. Comb. 15 (2008)  R94  ( pdf file 155 kb)

A. Rahnamai Barghi and John D. Dixon, Irreducible characters which are zero on only one conjugacy class, Proc. Amer.  Math. Soc. 135 (2007) 41-45    (pdf file 113 kb)

John D. Dixon, Asymptotics of generating the symmetric and alternating groups, Electronic J. Comb. 12 (2005) R56. ( pdf file 117 kb)
John D. Dixon,
Permutation representations and rational irreducibility, Bull. Austral. Math. Soc. 71 (2005) 493-503.  (pdf file 174 kb)

A. Rahnamai Barghi and John D. Dixon,  Degree homogeneous groups, Canad. Math. Bull. 48 (2005) 41-49. ( pdf file  197 kb)

John D. Dixon and Daniel Panario, The degree of the splitting field of a random polynomial over a finite field, Electronic J. Comb. 11 (2004) R70    ( pdf file  180 kb)

John D. Dixon and A. Dubickas, The values of Mahler measures, Mathematika 51 (2004) 131-148.   ( pdf file   210 kb)

J.D. Dixon and A.E. Zalesski,  Finite imprimitive linear groups of prime degree, J. Algebra 276 (2004) 340-370. ( pdf file  308 kb)

J.D. Dixon, L. Pyber, A. Seress and A. Shalev,  Residual properties of free groups and probabilistic methods, J. reine angew. Math. 556 (2003) 159-172. ( pdf file  173 kb)

John D. Dixon, Probabilistic group theory,  C.R. Math. Rep. Acad.. Sci. Canada 24 (2002) 1-15.  ( pdf file   205 kb)

J.D. Dixon and A.E. Zalesskii, Finite primitive groups of prime degree, J. London Math. Soc.  (2) 57 (1998) 126-134; errata:  in J. London Math. Soc. (2008)  ( pdf file 105 kb) 

John D. Dixon, Groups with a Cayley graph isomorphic to a hypercube, Bull. Austral. Math. Soc. 55 (1997) 385-393

John D. Dixon and Brian Mortimer, "Permutation Groups", Springer-Verlag (GTM 163) 1996

J.D. Dixon, M. du Sautoy, A. Mann and D. Segal, "Analytic Pro-p Groups", Cambridge Univ. Press (LMS Lecture Notes 157) 1991 (second ed. 1999)

John D. Dixon, Most finitely generated permutation groups are free, Bull. London Math. Soc. 22 (1990) 222-226

John D. Dixon and Brian Mortimer, Primitive permutation groups of degree less than 1000, Proc. Camb. Philos. Soc. 103 (1988) 213-238

John D. Dixon, The Tits alternative (pdf file 149 kb)

John D. Dixon, Estimating extremal eigenvalues and condition numbers, SIAM J. Numer. Anal. 20 (1983) 812-814 JSTOR

John D. Dixon, Asymptotically fast factorization of integers, Math. Comput. 36 (1981) 256-260 JSTOR

John D. Dixon, A brief proof of Cauchy's integral theorem, Proc. Amer. Math. Soc. 29 (1972) 625-626

Errata to the book "Permutation Groups"
Introduction to Coding Theory
Slides for a talk on the Riemann Hypothesis Riemann's Insight (pdf file 1027 kb)