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Cyclic, Separable and Semisimple Matrices in the Special Linear Groups Over a Finite Field
Author(s) -
Britnell John R.
Publication year - 2002
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/s0024610702003678
Subject(s) - mathematics , separable space , finite field , field (mathematics) , matrix (chemical analysis) , set (abstract data type) , polynomial , pure mathematics , combinatorics , algebra over a field , discrete mathematics , computer science , mathematical analysis , chemistry , chromatography , programming language
A matrix A with minimum polynomial m A and characteristic polynomial c A is said to be cyclic if m A = c A , semisimple if m A has no repeated factors, and separable if it is both cyclic and semisimple. For any set T of matrices, we write C T for the proportion of cyclic matrices in T , SS T for the proportion of semisimple matrices, and S T for the proportion of separable matrices. We will write C GL(∞, q ) for lim d→∞ C GL( d , q ) , and so on.