منابع مشابه
Automorphism Groups of Simple Moufang Loops over Perfect Fields
Let F be a perfect field and M(F ) the nonassociative simple Moufang loop consisting of the units in the (unique) split octonion algebra O(F ) modulo the center. Then Aut(M(F )) is equal to G2(F )o Aut(F ). In particular, every automorphism of M(F ) is induced by a semilinear automorphism of O(F ). The proof combines results and methods from geometrical loop theory, groups of Lie type and compo...
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Let F be a finite field or a local field of any characteristic. If A is a finite dimensional associative nilpotent algebra over F , the set 1 +A of all formal expressions of the form 1 +x, where x ∈ A, is a locally compact group with the topology induced by the standard one on F and the multiplication (1 + x) · (1 + y) = 1 + (x + y + xy). We prove a result conjectured by E. Gutkin in 1973: ever...
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Let K be a locally compact field and G a simple AT-group, G = G(K). A discrete subgroup T of G is called a lattice if G/F carries a finite G-invariant measure. It is a uniform (or cocompact) lattice if G/T is compact and nonuniform otherwise. When the jRf-rank of G is greater than one, Margulis [Ma, Z] proved that T is arithmetic, establishing the conjecture of Selberg and PiatetskiShapiro. Thi...
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ژورنال
عنوان ژورنال: Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial
سال: 2018
ISSN: 2640-7345,2640-7337
DOI: 10.2140/iig.2018.16.159