The graph extension theorem
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- by Ernest Shult PDF
- Proc. Amer. Math. Soc. 33 (1972), 278-284 Request permission
Abstract:
A sufficient condition is given that a transitive permutation group G admits a transitive extension ${G^\ast }$. The condition is graph-theoretic and does not involve any direct algebraic properties of the group being extended. The result accounts for a fairly wide class of doubly transitive groups, including the two doubly transitive representations of the groups ${\text {Sp}}(2n,2)$, and the doubly transitive representations of the Higman-Sims group, and the Conway group (.3).References
- J. H. Conway, A group of order $8,315,553,613,086,720,000$, Bull. London Math. Soc. 1 (1969), 79–88. MR 248216, DOI 10.1112/blms/1.1.79
- Graham Higman, On the simple group of D. G. Higman and C. C. Sims, Illinois J. Math. 13 (1969), 74–80. MR 240193
- D. G. Higman, Solvability of a class of rank $3$ permutation groups, Nagoya Math. J. 41 (1971), 89–96. MR 276316
- Jack McLaughlin, A simple group of order $898,128,000$, Theory of Finite Groups (Symposium, Harvard Univ., Cambridge, Mass., 1968), Benjamin, New York, 1969, pp. 109–111. MR 0242941
- Ernest E. Shult, Characterizations of certain classes of graphs, J. Combinatorial Theory Ser. B 13 (1972), 142–167. MR 311518, DOI 10.1016/0095-8956(72)90050-0 —, Supplement to “The graph extension theorem", University of Florida, Gainesville, Fla. (mimeographed notes).
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 33 (1972), 278-284
- MSC: Primary 20B99
- DOI: https://doi.org/10.1090/S0002-9939-1972-0294477-5
- MathSciNet review: 0294477