Generating finite completely reducible linear groups
نویسندگان
چکیده
منابع مشابه
Generating Finite Completely Reducible Linear Groups
It is proved here that each finite completely reducible linear group of dimension d (over an arbitrary field) can be generated by L 3 d] elements. If a finite linear group G of dimension d is not completely reducible, then its characteristic is a prime, p say, and the factor group of G modulo the largest normal p-subgroup O.p(G) may be viewed as a completely reducible linear group acting on the...
متن کاملCompletely Reducible p-compact Groups
Rational automorphisms of products of simple p-compact groups are shown to be composites of products of rational automorphisms of the individual factors and permutation maps.
متن کاملOn Finite Simply Reducible Groups
A finite group G is said to be simply reducible (SR-group) if it has the following two properties: 1) each element of G is conjugate to its inverse; 2) the tensor product of every two irreducible representations is decomposed as a sum of irreducible representations of G with multiplicities not exceeding 1. It is proved that a finite SR-group is solvable if it has no composition factors isomorph...
متن کاملComputing Galois Groups of Completely Reducible Differential Equations
At present we do not know a general algorithm that will compute the Galois group of a linear differential equation with coefficients in a differential field k, even when k = Q̄(x), where Q̄ is the algebraic closure of the rational numbers. In contrast, algorithms for calculating the Galois group of a polynomial with coefficients in Q or Q̄(x) have been known for a long time (van der Waerden, 1953;...
متن کاملCompletely reducible sets
We study the family of rational sets of words, called completely reducible and which are such that the syntactic representation of their characteristic series is completely reducible. This family contains, by a result of Reutenauer, the submonoids generated by bifix codes and, by a result of Berstel and Reutenauer, the cyclic sets. We study the closure properties of this family. We prove a resu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1991
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1991-1047004-0