Research Interests

My research interests lie in Computational Algebra, Representation Theory, Group Theory, Combinatorics, and Experimental Mathematics.


Publications

My publications are (mostly) below, in pdf, or ps, or dvi formats. For reviews of my papers, follow the MR (Mathematical Reviews) or Zbl (Zentralblatt) links. Advice on writing: DG | JRS | DEK | KT.


Proportion of cyclic matrices in maximal reducible matrix algebras (with Scott Brown, Michael Giudici, and Cheryl E. Praeger ), to appear J. Algebra. pdf

Distant parents in complete binary trees, to appear Math. Scientist. pdf

p-groups having a unique proper nontrivial characteristic subgroup (with Csaba Schneider and P.P. Pálfy), J. Algebra 348 (2011), 85--109. pdf

Enumerating the rationals from left to right, Amer. Math. Monthly 118 (2011), 830--835. pdf

Towards an efficient Meat-axe algorithm using f-cyclic matrices: the density of uncyclic matrices in M(n,q) (with Cheryl E. Praeger ), J. Algebra 322 (2009), 766--790. pdf | dvi | MR | Zbl
Appendix 1 The polynomials unc(n,q) for n ≤ 37. Appendix 2 Magma computer programs for verifying Conjecture 3 for small n.
PhD thesis Sophie Ambrose, School of Mathematics and Statistics, University of Western Australia, 2006.

Worms by number (with C.J. Glasby and F. Pleijel ) Proc. Royal Soc. B 295 (2008), 2071--2076. pdf | ProcRoyalSocBpdf

Writing representations over proper division subrings, J. Algebra 319 (2008), 77--92. ps | pdf | MR | Zbl

The shape of solvable groups with odd order, in: Groups St Andrews 2005, vol. 2, Edited by C.M. Campbell, M.R. Quick, E.F. Robertson and G.C. Smith, London Mathematical Society Lecture Notes Series 340, Cambridge Univ. Press, (2007), 432--437. ps | pdf | MR | Zbl

The Meat-axe and f-cyclic matrices J. Algebra 300 (2006), 77--90. ps | pdf | MR | Zbl

Writing projective representations over proper subfields (with C.R. Leedham-Green and E.A. O'Brien ) J. Algebra 295 (2006), 51--61. ps | pdf | MR| Zbl

Solvable groups with a given solvable length, and minimal composition length, J. Group Theory 8 (2005), 339--350. ps | pdf | MR | Zbl

Modules induced from a normal subgroup of prime index, in Rings, Modules, and Abelian Groups, Eds. A. Facchini, E. Houston and L. Salce, Lecture Notes in Pure and Applied Mathematics 236 (2004), 257--270. ps | pdf | MR | Zbl

On the tensor product of polynomials over a ring, J. Austral. Math. Soc. 71 (2001), 1--17. ps | pdf | MR | Zbl

Using recurrence relations to count certain elements in symmetric groups, European J. Combin. 22 (2001), 497--501. ps | pdf | MR | Zbl

Extended Euclid's algorithm via backward recurrence relations, Math. Mag. 75 (1999), 228--230. ps | pdf | Zbl

Subgroups of the upper-triangular matrix group with maximal derived length and a minimal number of generators, in Groups St Andrews 1997 in Bath, I, Edited by C.M. Campbell et al., London Mathematical Society Lecture Notes Series 260, Cambridge Univ. Press, (1999), 275--281. ps | pdf | MR| Zbl

Writing representations over minimal fields (with R.B. Howlett ), Comm. Algebra 25 (1997), 1703--1712. ps | pdf | MR | Zbl

Irreducible modules and normal subgroups of prime index (with L.G. Kovács ), Comm. Algebra 24 (1996), 1529--1546. ps | pdf | MR| Zbl

On generators for the group of units of the ring of integers modulo n, Austral. Math. Soc. Gaz. 22 (1995), 226--228. ps | pdf | MR| Zbl

On the faithful representations, of degree 2n, of certain extensions of 2-groups by orthogonal or symplectic groups, J. Austral. Math. Soc. Ser. A 58 (1995), 232--247. ps | pdf | MR| Zbl

Extraspecial towers and Weil representations (with R.B. Howlett ), J. Algebra 151 (1992), 236--260. ps | pdf | MR| Zbl

Computing intersections and normalizers in soluble groups (with M.C. Slattery ), J. Symbolic Comput. 9 (1990), 637--651. ps | pdf | MR| Zbl

The composition and derived lengths of a finite soluble group, J. Algebra 120 (1989), 406--413. ps | pdf | MR| Zbl

Constructing normalisers in finite soluble groups, J. Symolic Comput. 5 (1988), 285--294. ps | pdf | MR| Zbl

Intersecting subgroups of finite soluble groups. J. Symbolic Comput. 5 (1988), 295--301. MR| Zbl (Reprint available upon request.)

2-groups with every automorphism central. J. Austral. Math. Soc. Ser. A 41 (1986), 233--236. pdf | MR| Zbl

Books

An Introduction to Computational Mathematics (book in preparation.)

Algebra, A First Year Text (with W.G. Gibson and J. Henderson) (The Univ. of Sydney, 1993, 202pp., revised in 1999.)

Jackson and Sasha go Camping: a children's book (2010, 12pp., 7 illustrations).


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