Group theory

Topics Some of my publications

Finite Abelian groups and their duals
R. A. Bailey: Patterns of confounding in factorial designs. Biometrika 64 (1977), 597–603. doi: 10.1093/biomet/64.3.597 [Maths Reviews 0501643 (58 #18945)]
R. A. Bailey: Dual Abelian groups in the design of experiments. In Algebraic Structures and Applications (eds. P. Schultz, C. E. Praeger and R. P. Sullivan), Marcel Dekker, New York, 1982, pp. 45–54. [Maths Reviews 0647165 (83m: 62135)]
R. A. Bailey: Factorial design and Abelian groups. Linear Algebra and its Applications 70 (1985), 349–368. doi: 10.1016/0024-3795(85)90064-3 [Maths Reviews 0808552 (87c: 62151)]
R. A. Bailey: Cyclic designs and factorial designs. In Probability, Statistics and Design of Experiments (proceedings of the R. C. Bose Symposium on Probability, Statistics and Design of Experiments, Delhi, 27–30 December, 1988) (ed. R. R. Bahadur), Wiley Eastern, New Delhi, 1990, pp. 51–74.

Which combinatorial objects have a group of automorphisms whose permutation character is multiplicity-free?
R. A. Bailey: Latin squares with highly transitive automorphism groups. Journal of the Australian Mathematical Society, Series A 33 (1982), 18–22. doi: 10.1017/S1446788700017560 [Maths Reviews 0662355 (83g: 05021)]
R. A. Bailey, Cheryl E. Praeger, C. A. Rowley and T. P. Speed: Generalized wreath products of permutation groups. Proceedings of the London Mathematical Society 47 (1983), 69–82. doi: 10.1112/plms/s3-47.1.69 [Maths Reviews 0698928 (85b: 20005)]
P. P. Alejandro, R. A. Bailey and P. J. Cameron: Association schemes and permutation groups. Discrete Mathematics 266 (2003), 47–67. doi:10.1016/S0012-365X(02)00798-7 [Maths Reviews 1991706 (2004c: 05216)]

What are useful ways of generalizing the direct and wreath products as methods of combining permutation groups?
R. A. Bailey, Cheryl E. Praeger, C. A. Rowley and T. P. Speed: Generalized wreath products of permutation groups. Proceedings of the London Mathematical Society 47 (1983), 69–82. doi: 10.1112/plms/s3-47.1.69 [Maths Reviews 0698928 (85b: 20005)]
R. A. Bailey and Peter J. Cameron: Crested products of association schemes. Journal of the London Mathematical Society 72 (2005), 1–24. doi: 10.1112/S0024610705006666 [Maths Reviews 2145725 (2006h: 05240)]

Which finite groups have terraces?
R. A. Bailey: Quasi-complete Latin squares: construction and randomization. Journal of the Royal Statistical Society, Series B 46 (1984), 323–334. doi: 10.1111/j.2517-6161.1984.tb01305.x [Maths Reviews 0781893 (86i: 62161)]
R. A. Bailey and Cheryl E. Praeger: Directed terraces for direct product groups. Ars Combinatoria 25A (1988), 73–76. [Maths Reviews 0942492 (89i: 20041)]
Ian Anderson and R. A. Bailey: Completeness properties of conjugates of Latin squares based on groups, and an application to bipartite tournaments. Bulletin of the Institute of Combinatorics and its Applications 21 (1997), 95–99. [Maths Reviews 1470311 (98d: 05032)]

What can we learn about a design from its automorphism group?
R. A. Bailey: Contribution to the discussion of `Symmetry models and hypotheses for structured data layouts' by A. P. Dawid. Journal of the Royal Statistical Society, Series B 50 (1988), pp. 22–24.
R. A. Bailey: Automorphism groups of block structures with and without treatments. In Coding Theory and Design Theory. Part II: Design Theory (ed. D. Ray-Chaudhuri), IMA Volumes in Mathematics and its Applications, 21, Springer-Verlag, New York, 1990, pp. 24–41. [Maths Reviews 1056523 (91g: 05011)]
R. A. Bailey and C. A. Rowley: General balance and treatment permutations. Linear Algebra and its Applications 127 (1990), 183–225. doi: 10.1016/0024-3795(90)90343-B [Maths Reviews 1048802 (91d: 05014)]
R. A. Bailey: Contribution to the discussion of `Invariance and factorial models' by P. McCullagh. Journal of the Royal Statistical Society, Series B 62 (2000), pp. 239–241.

Automorphism groups of combinatorial structures
R. A. Bailey: Distributive block structures and their automorphisms. In Combinatorial Mathematics VIII (ed. K. L. McAvaney), Lecture Notes in Mathematics, 884 Springer-Verlag, Berlin, 1981, pp. 115–124. doi: 10.1007/BFb0091813 [Maths Reviews 0641241 (83c: 62119)]
R. A. Bailey: Latin squares with highly transitive automorphism groups. Journal of the Australian Mathematical Society, Series A 33 (1982), 18–22. doi: 10.1017/S1446788700017560 [Maths Reviews 0662355 (83g: 05021)]
R. A. Bailey and D. Jungnickel: Translation nets and fixed-point-free group automorphisms. Journal of Combinatorial Theory, Series A 55 (1990), 1–13. doi: 10.1016/0097-3165(90)90043-V [Maths Reviews 1070011 (91h: 05030)]
R. A. Bailey: A Howell design admitting A₅. Discrete Mathematics 167-168 (1997), 65–71. doi: 10.1016/S0012-365X(96)00216-6 [Maths Reviews 1446733 (98h: 05039)]
Ian Anderson and R. A. Bailey: Completeness properties of conjugates of Latin squares based on groups, and an application to bipartite tournaments. Bulletin of the Institute of Combinatorics and its Applications 21 (1997), 95–99. [Maths Reviews 1470311 (98d: 05032)]
R. A. Bailey, M. Buratti, G. Rinaldi and T. Traetta: On 2-pyramidal Hamiltonian cycle systems. Bulletin of the Belgian Mathematical Society—Simon Stevin, 21 (2014), 747–758. doi: 10.36045/bbms/1414091012

Statistical models invariant under a group of permutations
R. A. Bailey: Contribution to the discussion of `Symmetry models and hypotheses for structured data layouts' by A. P. Dawid. Journal of the Royal Statistical Society, Series B 50 (1988), pp. 22-24.
R. A. Bailey: Contribution to the discussion of `Invariance and factorial models' by P. McCullagh. Journal of the Royal Statistical Society, Series B 62 (2000), pp. 239-241.
R. A. Bailey, Persi Diaconis, Daniel N. Rockmore and Chris Rowley: A spectral analysis approach for experimental designs. In Excursions in Harmonic Analysis, Volume 4 (eds. R. Balan, M. Begué, J. J. Benedetto, W. Czaja and K. A. Okoudjou), Springer International Publishing (2015), pp. 367–395. doi: 10.1007/978-3-319-20188-7_14

Groups generated by derangements
R. A. Bailey, Peter J. Cameron, Michael Giudici and Gordon Royle: Groups generated by derangements. Journal of Algebra, 572 (2021), 245–262. doi: 10.1016/j.jalgebra.2020.12.020

Diagonal groups
R. A. Bailey, Peter J. Cameron, Cheryl E. Praeger and Csaba Schneider: The geometry of diagonal groups. Transactions of the American Mathematical Society, 375 (2022), 5259–5311. doi: 10.1090/tran/8507
R. A. Bailey, Peter J. Cameron, Michael Kinyon and Cheryl E. Praeger: Diagonal groups and arcs over groups. Designs, Codes and Cryptography, 90 (2022), 2069–2080. doi: 10.1007/s10623-021-00907-2 [Maths Reviews 4473950]

Topics	Some of my publications
Finite Abelian groups and their duals	R. A. Bailey: Patterns of confounding in factorial designs. Biometrika 64 (1977), 597–603. doi: 10.1093/biomet/64.3.597 [Maths Reviews 0501643 (58 #18945)] R. A. Bailey: Dual Abelian groups in the design of experiments. In Algebraic Structures and Applications (eds. P. Schultz, C. E. Praeger and R. P. Sullivan), Marcel Dekker, New York, 1982, pp. 45–54. [Maths Reviews 0647165 (83m: 62135)] R. A. Bailey: Factorial design and Abelian groups. Linear Algebra and its Applications 70 (1985), 349–368. doi: 10.1016/0024-3795(85)90064-3 [Maths Reviews 0808552 (87c: 62151)] R. A. Bailey: Cyclic designs and factorial designs. In Probability, Statistics and Design of Experiments (proceedings of the R. C. Bose Symposium on Probability, Statistics and Design of Experiments, Delhi, 27–30 December, 1988) (ed. R. R. Bahadur), Wiley Eastern, New Delhi, 1990, pp. 51–74.
Which combinatorial objects have a group of automorphisms whose permutation character is multiplicity-free?	R. A. Bailey: Latin squares with highly transitive automorphism groups. Journal of the Australian Mathematical Society, Series A 33 (1982), 18–22. doi: 10.1017/S1446788700017560 [Maths Reviews 0662355 (83g: 05021)] R. A. Bailey, Cheryl E. Praeger, C. A. Rowley and T. P. Speed: Generalized wreath products of permutation groups. Proceedings of the London Mathematical Society 47 (1983), 69–82. doi: 10.1112/plms/s3-47.1.69 [Maths Reviews 0698928 (85b: 20005)] P. P. Alejandro, R. A. Bailey and P. J. Cameron: Association schemes and permutation groups. Discrete Mathematics 266 (2003), 47–67. doi:10.1016/S0012-365X(02)00798-7 [Maths Reviews 1991706 (2004c: 05216)]
What are useful ways of generalizing the direct and wreath products as methods of combining permutation groups?	R. A. Bailey, Cheryl E. Praeger, C. A. Rowley and T. P. Speed: Generalized wreath products of permutation groups. Proceedings of the London Mathematical Society 47 (1983), 69–82. doi: 10.1112/plms/s3-47.1.69 [Maths Reviews 0698928 (85b: 20005)] R. A. Bailey and Peter J. Cameron: Crested products of association schemes. Journal of the London Mathematical Society 72 (2005), 1–24. doi: 10.1112/S0024610705006666 [Maths Reviews 2145725 (2006h: 05240)]
Which finite groups have terraces?	R. A. Bailey: Quasi-complete Latin squares: construction and randomization. Journal of the Royal Statistical Society, Series B 46 (1984), 323–334. doi: 10.1111/j.2517-6161.1984.tb01305.x [Maths Reviews 0781893 (86i: 62161)] R. A. Bailey and Cheryl E. Praeger: Directed terraces for direct product groups. Ars Combinatoria 25A (1988), 73–76. [Maths Reviews 0942492 (89i: 20041)] Ian Anderson and R. A. Bailey: Completeness properties of conjugates of Latin squares based on groups, and an application to bipartite tournaments. Bulletin of the Institute of Combinatorics and its Applications 21 (1997), 95–99. [Maths Reviews 1470311 (98d: 05032)]
What can we learn about a design from its automorphism group?	R. A. Bailey: Contribution to the discussion of `Symmetry models and hypotheses for structured data layouts' by A. P. Dawid. Journal of the Royal Statistical Society, Series B 50 (1988), pp. 22–24. R. A. Bailey: Automorphism groups of block structures with and without treatments. In Coding Theory and Design Theory. Part II: Design Theory (ed. D. Ray-Chaudhuri), IMA Volumes in Mathematics and its Applications, 21, Springer-Verlag, New York, 1990, pp. 24–41. [Maths Reviews 1056523 (91g: 05011)] R. A. Bailey and C. A. Rowley: General balance and treatment permutations. Linear Algebra and its Applications 127 (1990), 183–225. doi: 10.1016/0024-3795(90)90343-B [Maths Reviews 1048802 (91d: 05014)] R. A. Bailey: Contribution to the discussion of `Invariance and factorial models' by P. McCullagh. Journal of the Royal Statistical Society, Series B 62 (2000), pp. 239–241.
Automorphism groups of combinatorial structures	R. A. Bailey: Distributive block structures and their automorphisms. In Combinatorial Mathematics VIII (ed. K. L. McAvaney), Lecture Notes in Mathematics, 884 Springer-Verlag, Berlin, 1981, pp. 115–124. doi: 10.1007/BFb0091813 [Maths Reviews 0641241 (83c: 62119)] R. A. Bailey: Latin squares with highly transitive automorphism groups. Journal of the Australian Mathematical Society, Series A 33 (1982), 18–22. doi: 10.1017/S1446788700017560 [Maths Reviews 0662355 (83g: 05021)] R. A. Bailey and D. Jungnickel: Translation nets and fixed-point-free group automorphisms. Journal of Combinatorial Theory, Series A 55 (1990), 1–13. doi: 10.1016/0097-3165(90)90043-V [Maths Reviews 1070011 (91h: 05030)] R. A. Bailey: A Howell design admitting A₅. Discrete Mathematics 167-168 (1997), 65–71. doi: 10.1016/S0012-365X(96)00216-6 [Maths Reviews 1446733 (98h: 05039)] Ian Anderson and R. A. Bailey: Completeness properties of conjugates of Latin squares based on groups, and an application to bipartite tournaments. Bulletin of the Institute of Combinatorics and its Applications 21 (1997), 95–99. [Maths Reviews 1470311 (98d: 05032)] R. A. Bailey, M. Buratti, G. Rinaldi and T. Traetta: On 2-pyramidal Hamiltonian cycle systems. Bulletin of the Belgian Mathematical Society—Simon Stevin, 21 (2014), 747–758. doi: 10.36045/bbms/1414091012
Statistical models invariant under a group of permutations	R. A. Bailey: Contribution to the discussion of `Symmetry models and hypotheses for structured data layouts' by A. P. Dawid. Journal of the Royal Statistical Society, Series B 50 (1988), pp. 22-24. R. A. Bailey: Contribution to the discussion of `Invariance and factorial models' by P. McCullagh. Journal of the Royal Statistical Society, Series B 62 (2000), pp. 239-241. R. A. Bailey, Persi Diaconis, Daniel N. Rockmore and Chris Rowley: A spectral analysis approach for experimental designs. In Excursions in Harmonic Analysis, Volume 4 (eds. R. Balan, M. Begué, J. J. Benedetto, W. Czaja and K. A. Okoudjou), Springer International Publishing (2015), pp. 367–395. doi: 10.1007/978-3-319-20188-7_14
Groups generated by derangements	R. A. Bailey, Peter J. Cameron, Michael Giudici and Gordon Royle: Groups generated by derangements. Journal of Algebra, 572 (2021), 245–262. doi: 10.1016/j.jalgebra.2020.12.020
Diagonal groups	R. A. Bailey, Peter J. Cameron, Cheryl E. Praeger and Csaba Schneider: The geometry of diagonal groups. Transactions of the American Mathematical Society, 375 (2022), 5259–5311. doi: 10.1090/tran/8507 R. A. Bailey, Peter J. Cameron, Michael Kinyon and Cheryl E. Praeger: Diagonal groups and arcs over groups. Designs, Codes and Cryptography, 90 (2022), 2069–2080. doi: 10.1007/s10623-021-00907-2 [Maths Reviews 4473950]

Page maintained by R. A. Bailey