Proceedings of the American Mathematical Society

Author(s): Cai Heng Li
Journal: Proc. Amer. Math. Soc. 136 (2008), 1905-1910.
MSC (2000): Primary 05C25
Posted: February 14, 2008
Retrieve article in: PDF DVI PostScript

Abstract: It is shown that for a connected cubic graph $\mathit{\Gamma}$ , a vertex transitive group $G\le{\sf {Aut}}\,{\mathit{\Gamma}}$ contains a large semiregular subgroup. This confirms a conjecture of Cameron and Sheehan (2001).

1.: P. J. Cameron (ed.), Problems from the Seventeenth British Combinatorial Conference, Discrete Math. 231 (2001), 469-478.
2.: P. Cameron, M. Giudici, G. Jones, W. Kantor, M. Klin, D. Marušič and L. Nowitz, Transitive permutation groups without semiregular subgroups, J. London Math. Soc. (2) 66 (2002), 325-333. MR 1920405 (2003f:20001)
3.: P. Cameron, J. Sheehan and P. Spiga, Semiregular automorphisms of vertex-transitive cubic graphs, European J. Combin. 27 (2006), 924-930. MR 2226427 (2006m:05107)
4.: X. G. Fang, C. H. Li, and C. E. Praeger, The locally 2-arc-transitive graphs admitting a Ree simple group, J. Algebra 282 (2004), 638-666. MR 2101079 (2005j:05043)
5.: M. Giudici, Quasiprimitive groups with no fixed point free elements of prime order, J. London Math. Soc. (2) 67 (2003), no. 1, 73-84. MR 1942412 (2003m:20001)
6.: D. Marušič and R. Scapellato, Permutation groups, vertex-transitive digraphs and semiregular automorphisms, European J. Combin. 19 (1998). MR 1642726 (99g:05101)
7.: K. Zsigmondy, Zur Theorie der Potenzreste, Monatsh. Für Math. u. Phys. 3 (1892), 265-284. MR 1546236

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 05C25

Cai Heng Li
Affiliation: Department of Mathematics, Yunnan University, Kunming 650031, People's Republic of China; and School of Mathematics and Statistics, The University of Western Australia, Crawley 6009, WA, Australia
Email: li@maths.uwa.edu.au

DOI: 10.1090/S0002-9939-08-09217-4
PII: S 0002-9939(08)09217-4
Received by editor(s): September 5, 2005,
Received by editor(s) in revised form: June 1, 2006, and September 7, 2006
Posted: February 14, 2008
Additional Notes: This work was partially supported by an ARC Discovery Project Grant. The author is grateful to the referee for the constructive comments.
Communicated by: John R. Stembridge
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2008, American Mathematical Society Privacy Statement		Search the AMS