TY - JOUR UR - http://lib.ugent.be/catalog/pug01:161781 ID - pug01:161781 LA - eng TI - On generalized quadrangles with some concurrent axes of symmetry PY - 2002 JO - (2002) BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN SN - 1370-1444 PB - 2002 AU - Thas, Koen AB - Let S be a finite Generalized Quadrangle (GQ) of order (s, t), s not equal 1 not equal t, and suppose L is a line of S. A symmetry about L is an automorphism of S which fixes every line concurrent with L. A line L is an axis of symmetry if there is a full group of size s of symmetries about L. A point of a generalized quadrangle is a translation point if every line through it is an axis of symmetry. If there is a point p in a GQ S = (P, B, 1) for which there is a group G of automorphisms of the GQ which fixes p linewise, and such that G acts regularly on the points of P \ p(perpendicular to), then S is called an elation generalized quadrangle, and instead of S, often the notations (S-(P), G) or S(P) are used. If G is abelian, then (S-(P), G) is a translation generalized quadrangle (TGQ), and a GQ is a TGQ S-(P) if and only if p is a translation point, see [9]. We study the following two problems. (1) Suppose S is a G Q of order (8, t) s not equal 1 not equal t. How many distinct axes of symmetry through the same point p are needed to conclude that every line through p is an axis of symmetry, and hence that S-(P) is a TGQ? (2) Given a TGQ (S-(P), G), what is the minimum number of distinct lines through p such that G is generated by the symmetries about these lines? ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 161781 | ||
005 | 20180813141030.0 | ||
008 | 040114s2002------------------------eng-- | ||
022 | a 1370-1444 | ||
024 | a 000183864600007 2 wos | ||
024 | a 1854/LU-161781 2 handle | ||
040 | a UGent | ||
245 | a On generalized quadrangles with some concurrent axes of symmetry | ||
260 | c 2002 | ||
520 | a Let S be a finite Generalized Quadrangle (GQ) of order (s, t), s not equal 1 not equal t, and suppose L is a line of S. A symmetry about L is an automorphism of S which fixes every line concurrent with L. A line L is an axis of symmetry if there is a full group of size s of symmetries about L. A point of a generalized quadrangle is a translation point if every line through it is an axis of symmetry. If there is a point p in a GQ S = (P, B, 1) for which there is a group G of automorphisms of the GQ which fixes p linewise, and such that G acts regularly on the points of P \ p(perpendicular to), then S is called an elation generalized quadrangle, and instead of S, often the notations (S-(P), G) or S(P) are used. If G is abelian, then (S-(P), G) is a translation generalized quadrangle (TGQ), and a GQ is a TGQ S-(P) if and only if p is a translation point, see [9]. We study the following two problems. (1) Suppose S is a G Q of order (8, t) s not equal 1 not equal t. How many distinct axes of symmetry through the same point p are needed to conclude that every line through p is an axis of symmetry, and hence that S-(P) is a TGQ? (2) Given a TGQ (S-(P), G), what is the minimum number of distinct lines through p such that G is generated by the symmetries about these lines? | ||
598 | a A1 | ||
100 | a Thas, Koen u WE01 0 801001394231 | ||
650 | a Mathematics and Statistics | ||
653 | a axis of symmetry | ||
653 | a generalized quadrangle | ||
653 | a translation generalized quadrangle | ||
773 | t BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN g Bull. Belg. Math. Soc.-Simon Steven. 2002. 9 (2) p.217-243 q 9:2<217 | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/161781/file/763199 z [open] y Thas_2002_BBMS_9_2_217.pdf | ||
920 | a article | ||
Z30 | x WE 1 WE01 | ||
922 | a UGENT-WE |
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