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On Finite Line Transitive Affine Planes Whose Collineation Groups Contain no Baer Involutions

Published online by Cambridge University Press:  20 November 2018

Terry Czerwinski
Terry Czerwinski*
Affiliation:
University of Illinois at Chicago Circle, Chicago, Illinois
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A finite line transitive affine plane A is a finite plane which admits a collineation group G acting transitively on the set of all lines of A. Wagner [11] has shown that A is a translation plane and Hering [9] recently investigated the structure of A under the assumption that G has a composition factor isomorphic to a given nonabelian simple group. The purpose of this paper is to show that if the number of points on a line of A is odd, and if G contains no Baer involutions, then the hypothesis of Hering's Main Theorem holds.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 2 , 01 April 1975 , pp. 225 - 230
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Artin, E., Geometric algebra (Interscience Publishers, Inc., New York 1961).Google Scholar
2. Czerwinski, T., On collineation groups that fix a line of a finite projective plane (Submitted for publication).Google Scholar
3. Czerwinski, T., Collineation groups of finite projective planes whose Sylow 2-subgroups contain at most three involutions, Math. Z. 188 (1974), 161–170.Google Scholar
4. Dembowski, P., Finite geometries (Springer-Verlag, New York, 1968).Google Scholar
5. Foulser, D., Solvable flag transitive affine groups, Math. Z. 86 (1964), 191–204.Google Scholar
6. Gorenstein, D., Finite groups (Harper and Row, New York, 1968).Google Scholar
7. Greiss, R., Schur multipliers of the known finite simple groups, Ph.D. thesis, University of Chicago, 1972.Google Scholar
8. Hall, M., The theory of groups, (Macmillan, New York, 1959).Google Scholar
9. Hering, C., On finite line transitive affine planes (to appear).Google Scholar
10. Hering, C., On transitive linear groups (to appear).Google Scholar
11. Wagner, A., On finite affine line transitive planes, Math. Z. 87 (1965), 1–11.Google Scholar