Elations in translation planes of order 16
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In this article we prove the following: Let E denote the group generated by the set of all elations in a non-Desarguesian translation plane π of order 16. Then E is elementary abelian or dihedral of order 6 or 10. If ¦E¦=10 then the set of elation axes defines a derivable net contained in an E-invariant Desarguesian net of degree 7 and in this case π is the Hall plane. Thus, the only translation planes of order 16 to admit at least four elations with distinct axes are the Desarguesian and Hall planes.
KeywordsTranslation Plane Hall Plane Distinct Axis
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