Abstract
Locally projective graphs in Mathieu–Conway–Monster series appear in thin–thick pairs. A possible thick extension of a thin locally projective graph associated with the fourth Janko group has been questioned for a while. Such an extension could lead, if not to a new sporadic simple group, to something equally exciting. This paper resolves this issue ultimately in the non-existence form confirming that the list of 26 sporadic simple groups, although mysterious, is now stable. The result in fact concludes the classification project of locally projective graphs, which has been running for some twenty years.
Publisher
University of Zagreb, Faculty of Science, Department of Mathematics
Reference16 articles.
1. M. Giudici, A. A. Ivanov, L. Morgan and C. E. Praeger, A characterisation of weakly locally projective amalgams related to \(A_{16}\) and the sporadic simple groups \(M_{24}\) and \(He\), J. Algebra 460 (2016), 340-365.
2. W. Giuliano, Application of the amalgam method to the study of locally projective graphs, PhD Thesis, Imperial College London, 2022.
3. D. M. Goldschmidt, Automorphisms of trivalent graphs, Ann. of Math. (2) 111 (1980), 377-406.
4. A. A. Ivanov, The fourth Janko group, Oxford University Press, 2004.
5. A. A. Ivanov, The Mathieu groups, Cambridge Univ. Press, 2018.