PDFs of some of Chuck Miller's Papers and Notes

The word problem in quotients of a group

Miller, C. F. The word problem in quotients of a group, in Aspects of Effective Algebra, ed. J.N. Crossley, Proceedings of a conference at Monash University, August 1979, Upside Down A Book Company, Steel's Creek, (1981), 246-250. This paper was redone in TeX by the author with minimal alterations. See the postscript near the end concerning its history.

Some odd finitely presented groups

Baumslag, G and Miller, C. F., Some odd finitely presented groups, Bulletin of the London Math. Soc. 20 (1988), 239-244.

Decision problems for groups: survey and reflections

Miller, C. F., Decision problems for groups: survey and reflections, in Algorithms and Classification in Combinatorial Group Theory (eds. G Baumslag and C. F. Miller III), MSRI Publications No. 23, Springer-Verlag (1992), 1-59.

Strongly torsion generated groups

Berrick, A. J. and Miller, C. F., Strongly torsion generated groups, Math. Proc. Camb. Phil. Soc. 111 (1992), 219-229.

Isoperimetric inequalities and the homology of groups

Baumslag, G , Miller, C. F. and Short, H., Isoperimetric inequalities and the homology of groups, Invent. Math. 113 (1993), 531-560.

Unsolvable problems about small cancellation and word hyperbolic groups

Baumslag, G , Miller, C. F. and Short, H., Unsolvable problems about small cancellation and word hyperbolic groups, Bulletin of the London Math. Soc. 26 (1994), 97-101.

Finitely presented subgroups of automatic groups and their isoperimetric functions

Baumslag, G , Bridson, M., Miller, C. F. and Short, H., Finitely presented subgroups of automatic groups and their isoperimetric functions, Journal of the London Math. Soc. 56 (1997), 292-304.

Experimenting and computing with infinite groups

Baumslag, G. and Miller, C.F., Experimenting and computing with infinite groups, in DIMACS Series, volume 28, ``Groups and Computation II", (eds. W. Kantor and L. Finkelstein), Amer. Math. Soc. (1997), 19-30.

Solvable Baumslag-Solitar groups are not almost convex

Miller, C.F. and Shapiro, M., Solvable Baumslag-Solitar groups are not almost convex, Geom. Dedicata 72 (1998), 123-127.

The word problem in groups of cohomological dimension 2

Collins, D.J. and Miller, C.F., The word problem in groups of cohomological dimension 2, in the Groups St Andrews 1997 in Bath, I (eds. C.M. Campbell, E.F. Robertson, N.Ruskuc and G.C. Smith) London Math Soc. Lecture Notes 260, Cambridge University Press (1999), 211-218.

Some examples of hyperbolic groups

Miller, C.F., Neumann, W.D., Swarup, G.A., Some examples of hyperbolic groups, in Geometric Group Theory Down Under (eds. J. Cossey, C. F. Miller III, W. D. Neumann and M. Shapiro), de Gruyter Verlag (1999), 195-202.

Some presentations of the trivial group

Miller, C.F. and Schupp, P.E., Some presentations of the trivial group, in Groups, Languages and Geometry (editor R. H. Gilman), Contemporary Mathematics 250, Amer. Math. Soc. (1999), 113-115.

Fibre products, non-positive curvature and decision problems

Baumslag, G , Bridson, M., Miller, C. F. and Short, H., Fibre products, non-positive curvature and decision problems, Comment. Math. Helv. 75 (2000), 457-477.

Comment. Math. Helv. pdf version

The subgroups of direct products of surface groups

Bridson, M., Howie, J., Miller, C. F. and Short, H., The subgroups of direct products of surface groups, Geometriae Dedicata 92 (2002), 95-103.

Subgroups of a direct product with a free group

Miller, C. F., Subgroups of a direct product with a free group, Quarterly Journal of Maths 53 (2002), 503-506.

Finite presentation of fibre products of metabelian groups

Baumslag, G., Bridson, M., Holt, D. and Miller, C. F., Finite presentation of fibre products of metabelian groups, Journal of Pure and Applied Algebra. 181 (2003), 15-22.

Recognition of subgroups of direct products of hyperbolic groups

Bridson, M. R. and Miller, C. F., Recognition of subgroups of direct products of hyperbolic groups, Proc. Amer. Math. Soc. 132 (2004), 59-65.

The isomorphism problem for residually torsion-free nilpotent groups

Baumslag, G. and Miller, C. F., The isomorphism problem for residually torsion-free nilpotent groups, Groups, Geometry and Dynamics 1 (2007), 1-20.

Reflections on the residual finiteness of one-relator groups

Baumslag, G., Miller, C.F. and Troeger, D., Reflections on the residual finiteness of one-relator groups, Groups, Geometry and Dynamics 1 (2007), 209-219.

Finitely presented extensions by free groups

Baumslag, G. and Miller, C.F., Finitely presented extensions by free groups, Journal of Group Theory 10 (2007), 723-729.

Reflections on some groups of B.~H.~Neumann

Baumslag, G. and Miller, C.F., Reflections on some groups of B. H. Neumann, to appear in Journal of Group Theory (12 pages).

Structure and finiteness properties of subdirect products of groups

Bridson, M.R. and Miller, C.F., Structure and finiteness properties of subdirect products of groups, Proc. London Math. Soc. (3) 98 (2009), 631-651.

Subgroups of direct products of limit groups (or see abstract)

Bridson, M., Howie, J., Miller, C.F. and Short, H., Subgroups of direct products of limit groups, to appear in Annals of Mathematics (20 pages).

Finitely presented residually free groups (or see abstract)

Bridson, M., Howie, J., Miller, C.F. and Short, H., Finitely presented residually free groups, submitted for publication (38 pages).

Virtual properties of cyclically pinched one-relator groups

Baumslag, G., Fine, B., Miller, C.F. and Troeger, D., Virtual properties of cyclically pinched one-relator groups, Internat. Journal of Algebga and Computation 19 (2009), 213-227.

Various lecture notes:

Sets and Cardinality

C. F. Miller - lecture notes used in connection with an enrichment topic for first year mathematics students at the University of Melbourne. (21 pages)

Finite State Automata

C. F. Miller (with assistance from J. R. J. Groves, W. D. Neumann and D. Coulson) - lecture notes used in connection with various courses at the University of Melbourne (18 pages).

Combinatorial Group Theory

C. F. Miller - An early version of these notes was prepared for use by the participants in the Workshop on Algebra, Geometry and Topology held at the Australian National University, 22 January to 9 February, 1996. They have subsequently been updated and expanded many times for use by students in the subject 620-421 Combinatorial Group Theory at the University of Melbourne. Copyright 1996-2004 by C. F. Miller III. (about 100 pages)

Created: 22 March, 1999
Last modified: 9 June, 2009
Authorised by: C. F. Miller, Department of Mathematics and Statistics.