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A group theoretic characterization of Buekenhout‐Metz unitals
Author(s) -
Ebert G.L.,
Wantz K.
Publication year - 1996
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/(sici)1520-6610(1996)4:2<143::aid-jcd6>3.0.co;2-f
Subject(s) - mathematics , sylow theorems , unital , combinatorics , order (exchange) , collineation , semidirect product , conic section , characterization (materials science) , group (periodic table) , equivalence (formal languages) , pure mathematics , algebra over a field , finite group , projective test , projective space , physics , geometry , finance , quantum mechanics , optics , economics
It is shown that a unital U embedded in PG (2, q 2 ) is a Buekenhout‐Metz unital if and only if U admits a linear collineation group that is a semidirect product of a Sylow p ‐subgroup of order q 3 by a subgroup of order q − 1. This is the full linear collineation group of U except for two equivalence classes of unitals: (i) the classical unitals, and (ii) the Buekenhout‐Metz unitals which can be expressed as a union of a partial pencil of conics. The unitals in class (ii) only occur when q is odd, and any two of them are projectively equivalent. © 1996 John Wiley & Sons, Inc.