02785nam 22004335a 450 991015192750332120120613234500.03-03719-610-610.4171/110(CKB)3710000000953883(CH-001817-3)152-120613(PPN)178156116(EXLCZ)99371000000095388320120613j20120613 fy 0engurnn|mmmmamaatxtrdacontentcrdamediacrrdacarrierA Course on Elation Quadrangles[electronic resource] /Koen ThasZuerich, Switzerland European Mathematical Society Publishing House20121 online resource (129 pages)EMS Series of Lectures in Mathematics (ELM) ;2523-5176The notion of elation generalized quadrangle is a natural generalization to the theory of generalized quadrangles of the important notion of translation planes in the theory of projective planes. Almost any known class of finite generalized quadrangles can be constructed from a suitable class of elation quadrangles. In this book the author considers several aspects of the theory of elation generalized quadrangles. Special attention is given to local Moufang conditions on the foundational level, exploring for instance a question of Knarr from the 1990s concerning the very notion of elation quadrangles. All the known results on Kantor's prime power conjecture for finite elation quadrangles are gathered, some of them published here for the first time. The structural theory of elation quadrangles and their groups is heavily emphasized. Other related topics, such as p-modular cohomology, Heisenberg groups and existence problems for certain translation nets, are briefly touched. The text starts from scratch and is essentially self-contained. Many alternative proofs are given for known theorems. Containing dozens of exercises at various levels, from very easy to rather difficult, this course will stimulate undergraduate and graduate students to enter the fascinating and rich world of elation quadrangles. The more accomplished mathematician will especially find the final chapters challenging.Combinatorics & graph theorybicsscCombinatoricsmscGroup theory and generalizationsmscGeometrymscCombinatorics & graph theoryCombinatoricsGroup theory and generalizationsGeometry05-xx20-xx51-xxmscThas Koen726617ch0018173BOOK9910151927503321A Course on Elation Quadrangles2564802UNINA