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

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 2^{n}, 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

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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