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Remark to a Theorem Due to R. Sandler

Published online by Cambridge University Press:  20 November 2018

Oddvar Iden
Oddvar Iden*
Affiliation:
University of Bergen, Bergen, Norway
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To prove [2, Theorem 1], it is enough to remark that if x is a point or line of F4 which is fixed under H, then x is fixed under each subgroup of H. By Sylow's theorem, H has a subgroup H’ of order three. By [1, p. 420, Lemma 2.2], it follows that x is in the subplane of F4 generated by those elements of {A, B, C, D} which are fixed under H'. This subplane consists of a point only. Hence, x is in {A, B, C, D}, which is impossible. This argument can be used in many other cases.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 3 , 01 June 1970 , pp. 518
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Dembowski, P., Freie und offene projektive Ebenen, Math. Z. 72 (1960), 410–438.Google Scholar
2. Sandler, R., On finite collineation groups of F5 Can. J. Math. 21 (1969), 217–221.Google Scholar