Vol. 15, No. 1, 1965

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Collineation groups of semi-translation planes

Theodore G. Ostrom

Vol. 15 (1965), No. 1, 273–279

This paper consists in an investigation of the collineations of a class of planes constructed by the author. The construction consists of replacing the lines of a net embedded in a given plane by subplanes of the same net.

For the case in question, the given plane is the dual of a translation plane. The full collineation group of the new plane is isomorphic to a subgroup of the collineation group of the original plane. The main point of the argument is to show that the new planes admit no collineations displacing the line at infinity.

Mathematical Subject Classification
Primary: 50.70
Received: 28 January 1964
Published: 1 March 1965
Theodore G. Ostrom