Blueprint for the Classification of Translation Generalized Quadrangles

2006 ◽  
pp. 161-170
Keyword(s):  
Generalized Quadrangles

scholarly journals Classification of skew translation generalized quadrangles, I

2015 ◽  
Vol Vol. 17 no. 1 (Combinatorics) ◽  
Author(s):  
Koen Thas
Keyword(s):  
Generalized Quadrangles ◽  
New Classification ◽  
Open Problems ◽  
International Audience ◽  
Rank 2

Combinatorics International audience We describe new classification results in the theory of generalized quadrangles (= Tits-buildings of rank 2 and type B2), more precisely in the (large) subtheory of skew translation generalized quadrangles (``STGQs''). Some of these involve, and solve, long-standing open problems.

scholarly journals A classification of finite antiflag-transitive generalized quadrangles

2017 ◽  
Vol 370 (3) ◽  
pp. 1551-1601
Author(s):  
John Bamberg ◽  
Cai Heng Li ◽  
Eric Swartz
Keyword(s):  
Generalized Quadrangles

scholarly journals SIMPLE GROUPS, PRODUCT ACTIONS, AND GENERALIZED QUADRANGLES

2017 ◽  
Vol 234 ◽  
pp. 87-126
Author(s):  
JOHN BAMBERG ◽  
TOMASZ POPIEL ◽  
CHERYL E. PRAEGER
Keyword(s):  
Cartesian Product ◽  
Finite Geometry ◽  
Simple Groups ◽  
Generalized Quadrangles ◽  
Product Decomposition ◽  
Number Of Factors ◽  
Point Line ◽  
Set Of Points ◽  
Generic Assumption

The classification of flag-transitive generalized quadrangles is a long-standing open problem at the interface of finite geometry and permutation group theory. Given that all known flag-transitive generalized quadrangles are also point-primitive (up to point–line duality), it is likewise natural to seek a classification of the point-primitive examples. Working toward this aim, we are led to investigate generalized quadrangles that admit a collineation group$G$preserving a Cartesian product decomposition of the set of points. It is shown that, under a generic assumption on$G$, the number of factors of such a Cartesian product can be at most four. This result is then used to treat various types of primitive and quasiprimitive point actions. In particular, it is shown that$G$cannot haveholomorph compoundO’Nan–Scott type. Our arguments also pose purely group-theoretic questions about conjugacy classes in nonabelian finite simple groups and fixities of primitive permutation groups.

scholarly journals Classification of extended generalized quadrangles with maximum diameter

1992 ◽  
Vol 105 (1-3) ◽  
pp. 13-23 ◽  
Author(s):  
Alberto Del Fra ◽  
Dina Ghinelli
Keyword(s):  
Maximum Diameter ◽  
Generalized Quadrangles

Note on the spectral classification of carbon stars in the photographic infrared region

1966 ◽  
Vol 24 ◽  
pp. 21-23
Author(s):  
Y. Fujita
Keyword(s):  
Infrared Region ◽  
Spectral Classification ◽  
Carbon Stars

We have investigated the spectrograms (dispersion: 8Å/mm) in the photographic infrared region fromλ7500 toλ9000 of some carbon stars obtained by the coudé spectrograph of the 74-inch reflector attached to the Okayama Astrophysical Observatory. The names of the stars investigated are listed in Table 1.

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