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Commutators in Finite Simple Groups of Lie Type
Author(s) -
Gow Rod
Publication year - 2000
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609300007141
Subject(s) - mathematics , simple (philosophy) , type (biology) , pure mathematics , simple lie group , classification of finite simple groups , lie group , group of lie type , simple group , algebra over a field , group theory , ecology , philosophy , epistemology , biology
Using properties of the Steinberg character, we obtain a congruence modulo p for the number of ways in which a p ‐regular element may be expressed as a commutator in a finite simple group G of Lie type of characteristic p . This congruence shows that such an element is a commutator in G . We also show that if K and L are conjugacy classes of G consisting of elements whose centralizers have order relatively prime to p , then any p ‐regular element of G is expressible as the product of an element of K and an element of L . 1991 Mathematics Subject Classification 20C20, 20D08, 20G40.