Automorphism groups of compact projective planes

✍ Scribed by Theo Grundhofer

• Publisher: Springer
• Year: 1986
• Tongue: English
• Weight: 418 KB
• Volume: 21
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00181534

✦ Synopsis

Compact connected projective planes have been investigated extensively in the last 30 years, mostly by studying their automorphism groups. It is our aim here to remove the connectedness assumption in some general results of Salzmann [31] and H/ihl[14] on automorphism groups of compact projective planes. We show that the continuous collineations of every compact projective plane form a locally compact transformation group (Theorem 1), and that the continuous collineations fixing a quadrangle in a compact translation plane form a compact group (Corollary to Theorem 3). Furthermore we construct a metric for the topology of a quasifield belonging to a compact projective translation plane, using the modular function of its additive group (Theorem 2).