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Finite Primitive Linear Groups of Prime Degree
Author(s) -
Dixon J. D.,
Zalesskii A. E.
Publication year - 1998
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/s0024610798005778
Subject(s) - prime (order theory) , mathematics , monomial , degree (music) , combinatorics , finite field , lemma (botany) , finite group , simple group , classification of finite simple groups , simple (philosophy) , prime number , group (periodic table) , discrete mathematics , pure mathematics , group theory , group of lie type , physics , acoustics , ecology , philosophy , poaceae , epistemology , quantum mechanics , biology
Throughout this paper, r will denote a prime. Our object in this paper and another is to describe the finite irreducible subgroups of L ( r ):=SL( r , C), where C denotes the field of complex numbers. The cases for small degrees are known (see [ 14 ] for r =2 and r =3; [ 1 ] and [ 23–25 ] for r =5 and r =7; [ 13 , 18 ]). The imprimitive irreducible subgroups of L ( r ) are necessarily monomial because r is a prime, and we describe these in another paper [ 4 ]. In this paper, we show how the classification of finite simple groups can be used to classify the finite primitive groups of prime degree. Much of the necessary work has already been done by V. Landazuri and G. M. Seitz (see Lemma 1.3 below).