Publications and Research in Progress Dr. David A. Jackson

Publications Schur Multipliers of Some Finite Nilpotent Groups, Proc. Amer. Math. Soc. 66 (1977), 1-5. If you have access to MathSciNet and JSTOR, you can find a review of this paper on MathSciNet and a link to download the paper from JSTOR. Some One-Relator Semigroup Presentations with Soluble Word Problems, Math Proc. Camb. Philos. Soc. 99 (1986), 433-434. On the Invariance of Small Overlap Hypotheses, Semigroup Forum 43 (1991), 299-304. The Proportion of Fixed-Point-Free Elements of a Transitive Permutation Group, with N. Boston et al, Comm. Alg. 21 (1993), 3259-3275. [pdf file (208K)] The Membership Problem for < a,b : bab2 =ab > , Semigroup Forum 63 (2001), 63-70 [pdf file (126K)] Decision and Separability Problems for Baumslag-Solitar Semigroups, International Journal of Algebra and Computation 12 (2002), 33-49 [pdf file (216K)] Basic Commutators as Relators, with Anthony M. Gaglione and Dennis Spellman. J. Group Theory 5 (2002), 351-363 [Basic Commutators pdf file (180K)]

Accepted for Publication Basic Commutators in Weights Six and Seven as Relators, Accepted by Communications in Algebra, June 2007. [Weight Six pdf file (112K)]

Submitted for Publication Weight Five Basic Commutators as Relators, with Anthony M. Gaglione and Dennis Spellman. This was submitted to the New York Journal of Mathematics in fall 2001. [Weight Five pdf file (292K)] Ends for Cayley Digraphs of Semigroups and Monoids This is joint work with Vesna Kilibarda and contains several results that we consider both interesting and important. After working on this for at least four years, we submitted this to the Journal of the Australian Math Society in January 2007. [pdf file (692K)]

Research in Progress Uncountably Many Basic Sequences of Commutators This is a very easy result. Surprisingly, it does seem to be new. (Please tell me if you read this and it is previously known.) I regard this as more entertaining than actually useful. [pdf file (208K)] GLd(R) is not residually finite p: This is brief, but not necessarily a new result. Of particular interest is the case when R is the ring of p-adic integers. I have no immediate plans to submit this for publication. [pdf file (88K)] Achievable Relators: The work here is a reduction, using geometric methods, of the word problem for one-relator semigroups. (The word problem for one-relator semigroups is an important and difficult open question in the research area.) I have not actively worked on this for several years now, but I have distributed preliminary versions of this paper. This work is not currently complete. [pdf file (524K)]

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Last modified: 20 June, 2007