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)] Basic Commutators in Weights Six and Seven as Relators, Communications in Algebra, 36. [Weight Six pdf file (112K)]

Accepted for Publication 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. This has now been accepted for publication in the Journal of the Australian Math Society. We checked the page proofs in January 2009. The version below was revised in September 2008. [pdf file (692K)]

Submitted for Publication Weight Five Basic Commutators as Relators, with Anthony M. Gaglione and Dennis Spellman. This will soon be submitted to an AMS volume that Bob Morse is editing. It was submitted much earlier (fall 2001) to an electronic journal, but never found a referee who completed reading it. Alas. I have now fixed a very small flaw in the proof of the Basic Lemma. I have also added hyperlinks. These might be very useful to a reader who wants to see Lemma 3.10 again when it is used in the proof of Lemma 3.73 and for very numerous other such uses of previous lemmas in proofs. The hyperlinks seem to work fine in Acrobat and in Preview. For those who need to do without hyperlinks because they are reading the work in printed rather than electronic format, I have now included below the proofless version of the paper (so you can quickly find the statement of Lemma 3.10 while reading Lemma 3.73) and two of the most fundamentally useful lists of basic commutators (Use these as scoresheets to record the lemma which was used to prove that a given commutator was trivial in the natural quotient group.) [Weight Five pdf file (448K)] [Proofless Weight Five pdf file (128K)] [A scoresheet for the basic lemma in rank 3 (64K)] [A scoresheet for certain weight 6 basic commutators in rank 3 (64K)]

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: 24 February, 2009