Completions of Goldschmidt Amalgams of Type G4 in Dimension 3
Christopher Parker
and Peter Rowley
DOI: 10.1023/A:1008727918948
Abstract
The subgroups of GL 3( k) which are completions of the Goldschmidt G 4-amalgam are determined. We also draw attention to five related graphs which are remarkable in that they have large girth and few vertices.
Pages: 77–82
Keywords: finite groups; amalgams; completions; graphs
Full Text: PDF
References
1. N. Biggs, “Constructions for cubic graphs of large girth,” Electronic Journal of Combinatorics 5 (1998) A1.
2. D. Bloom, “The Subgroups of PSL3(q), for odd q,” Trans. Amer. Math. Soc. 127 (1967), 150-178.
3. J. Bray, C. Parker, and P. Rowley, “Cayley type graphs and cubic graphs of large girth,” Discrete Mathematics 214 (2000), 113-121.
4. D.M. Goldschmidt, “Automorphisms of trivalent graphs,” Ann. Math. 111 (1980), 377-404.
5. C. Parker and P. Rowley, “Finite completions of the Goldschmidt G3-amalgam and the Mathieu groups,” Manchester Centre for Pure Mathematics, preprint 1997/12.
6. C. Parker and P. Rowley, “Classical groups in Dimension 3 as completions of the Goldschmidt G3- amalgam,”Journal of LMS, to appear.
7. C. Parker and P. Rowley, “Sporadic simple groups and completions of the Goldschmidt G3-amalgam,” J. Alg. to appear.
2. D. Bloom, “The Subgroups of PSL3(q), for odd q,” Trans. Amer. Math. Soc. 127 (1967), 150-178.
3. J. Bray, C. Parker, and P. Rowley, “Cayley type graphs and cubic graphs of large girth,” Discrete Mathematics 214 (2000), 113-121.
4. D.M. Goldschmidt, “Automorphisms of trivalent graphs,” Ann. Math. 111 (1980), 377-404.
5. C. Parker and P. Rowley, “Finite completions of the Goldschmidt G3-amalgam and the Mathieu groups,” Manchester Centre for Pure Mathematics, preprint 1997/12.
6. C. Parker and P. Rowley, “Classical groups in Dimension 3 as completions of the Goldschmidt G3- amalgam,”Journal of LMS, to appear.
7. C. Parker and P. Rowley, “Sporadic simple groups and completions of the Goldschmidt G3-amalgam,” J. Alg. to appear.