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A Note on Groups of Ree Type

Published online by Cambridge University Press:  20 November 2018

Peter Lorimer
Peter Lorimer*
Affiliation:
University oF Auckland, Auckland, New Zealand
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The nonsolvable R-groups as defined by Walter [3] are groups of orders (q3+l)q3(q — 1), q = 32n+1, n ≥ 0. These are the groups of Ree type discussed by Ward [4] together with the Ree group R(3) of order 28.27.2. The R-group with parameter q has a doubly transitive representation of degree q3+1 but in this note we will prove that it cannot contain a sharply doubly transitive subset.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 3 , September 1973 , pp. 451 - 452
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Dembowski, P., Finite geometries, Springer-Verlag, Berlin, 1968.Google Scholar
2. Lorimer, P., A note on doubly transitive groups, J. Austral. Math. Soc. 6 (1966), 449–451.Google Scholar
3. Walter, J. H., Finite groups with abelian Sylow 2-subgroups of Order 8, Invent. Math. 2 (1967), 332–376.Google Scholar
4. Ward, H. N., On Ree’s series of simple groups, Trans. Amer. Math. Soc. 121 (1966), 62–89.Google Scholar