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 (2008), 2905-2909. [Weight Six pdf file (112K)] Ends for Cayley Digraphs of Semigroups and Monoids with Vesna Kilibarda. Journal of the Australian Math Society 87 (2009), 101-127. [pdf file (692K)] Weight Five Basic Commutators as Relators, with Anthony M. Gaglione and Dennis Spellman. Contemporary Mathematics 511 Computational Group Theory and the Theory of Groups, II, Kappe, Magidin and Morse, eds. (2010) 39-81. [Weight Five pdf file (448K)] Another Law for 3-Metabelian Groups, with Christine Bussman, the principal author. Glasgow Math. J. 54 (2012), 627-628. [W(x,y,z) is 3-Metabelian Law pdf file (40K)] A Solvable Conjugacy Problem for Finitely Presented C(3) Semigroups, with Paul Cummings, the principal author. Semigroup Forum 88 (2014), 52-66. [C(3) Conjugacy pdf file (560K)] Thickness of Feathers, with Paul Cummings. Communcations in Algebra 42 (12) (2014), 5329-5326. The file below is NOT the official version. I have a limited number of reprint downloads available if you ask. [Thickness of Feathers pdf file (923K)]

Research in Progress Axioms for Thickness, with Paul Cummings. We have submitted this twice and have had it rejected twice. I still think this is much better than that. In the Thickness of Feathers work above, we examined six different ways of defining the thickness of a feather, but did not state a definition for a thickness function. Here, we provide an axiomatic definition for a thickness function, examine general properties of all thickness functions, show that there are infinitely many distinct thickness functions and discuss some more restrictive concepts for thickness. A Solvable Conjugacy Problem for Finitely Presented Semigroups Satisfying C(2) and T(4), This is joint work with Paul Cummings. Paul is the lead author. Counting Patterns for Basic Commutators, The concept of a pattern for a basic commutator was introduced by C. Sims in Verifying Nilpotence in 1987. We provide counts for the number of patterns for all commutators in all basic sequences and for the number of patterns in one more structured collection of basic sequences. Weight Six Basic Commutators as Relators, The goal here is to prove that the normal closure in a non-Abelian free group of the set of basic commutators of weight six will NOT be the sixth term in the lower central series for the free group. This is work with Tony Ganglione and Dennis Spellman. The current approach is to attempt to examine this question in the variety where simple commutators of weight at least 4 commute with each other. 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. I plan to return to this work soon using the thickness concept as a tool. [pdf file (524K)]

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Last modified: 19 August, 2015