Premium
On Moore Geometries, I
Author(s) -
Damerell R. M.,
Georgiacodis M. A.
Publication year - 1981
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-23.1.1
Subject(s) - mathematics , field (mathematics) , quadratic equation , degree (music) , pure mathematics , geometry , polynomial , combinatorics , discrete mathematics , algebra over a field , mathematical analysis , physics , acoustics
In this paper it is proved that there are no non trivial Moore geometries of diameter > 12. The proof is based on a result of Fuglister, that if a Moore geometry exists, then the roots of a certain polynomial, called F d ( x ), are all rational or quadratic. We study F d ( x ) by examining its factors over the field Q 2 of 2‐adic numbers. In general F d ( x ) has an irreducible factor of degree ⩾ 3 in Q 2 [x], so the corresponding Moore geometry cannot exist.