منابع مشابه
Coverings of the smallest Paige loop
By investigating the construction of the split Cayley generalized hexagon, H(2), we get that there do not exist five distinct hexagon lines each a distance two apart from each other. From this we prove that the smallest Paige loop has a covering number of seven and that its automorphism group permutes these coverings transitively.
متن کاملOn the smallest simple, unipotent Bol loop
Finite simple, unipotent Bol loops have recently been identified and constructed using group theory. However, the purely group-theoretical constructions of the actual loops are indirect, somewhat arbitrary in places, and rely on computer calculations to a certain extent. In the spirit of revisionism, this paper is intended to give a more explicit combinatorial specification of the smallest simp...
متن کاملRemembrances of Bob Paige
I first met Bob in 1969. He had just come to New York to join the systems staff at the Courant Institute. We had a CDC6600 back then, but our computing services were in the dark ages. Bob was hired to debug a home-grown time sharing system that didn’t work. He turned out to be a perfect hire; Bob thoughtfully discarded the code and built the system afresh. Our acquaintance was casual for years....
متن کاملAn Appreciation of Bob Paige
As a senior faculty member of the Courant Institute at NYU since 1965 and a charter member of its Computer Science Department, founded in 1969, I knew Bob Paige as a graduate student and later as a colleague. My own area of expertise is mathematical logic, and so was only very peripherally connected with Bob’s work. But being directly involved with decisions about Bob’s faculty appointment and ...
متن کامل0 Products of all elements in a loop and a framework for non - associative analogues of the Hall - Paige conjecture
For a finite loop Q, let P (Q) be the set of elements that can be represented as a product containing each element of Q precisely once. Motivated by the recent proof of the Hall-Paige conjecture, we prove several universal implications between the following conditions: (A) Q has a complete mapping, i.e. the multiplication table of Q has a transversal, (B) there is no N EQ such that |N | is odd ...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2011
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-011-0284-6