The graph extension theorem

Author:
Ernest Shult

Journal:
Proc. Amer. Math. Soc. **33** (1972), 278-284

MSC:
Primary 20B99

MathSciNet review:
0294477

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Abstract: A sufficient condition is given that a transitive permutation group *G* admits a transitive extension . 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 , and the doubly transitive representations of the Higman-Sims group, and the Conway group (.3).

**[1]**J. H. Conway,*A group of order 8,315,553,613,086,720,000*, Bull. London Math. Soc.**1**(1969), 79–88. MR**0248216****[2]**Graham Higman,*On the simple group of D. G. Higman and C. C. Sims*, Illinois J. Math.**13**(1969), 74–80. MR**0240193****[3]**D. G. Higman,*Solvability of a class of rank 3 permutation groups*, Nagoya Math. J.**41**(1971), 89–96. MR**0276316****[4]**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****[5]**Ernest E. Shult,*Characterizations of certain classes of graphs*, J. Combinatorial Theory Ser. B**13**(1972), 142–167. MR**0311518****[6]**-,*Supplement to ``The graph extension theorem"*, University of Florida, Gainesville, Fla. (mimeographed notes).

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DOI:
https://doi.org/10.1090/S0002-9939-1972-0294477-5

Keywords:
Doubly transitive groups,
transitive extension,
automorphism groups of graphs

Article copyright:
© Copyright 1972
American Mathematical Society