 
Summary: Z .JOURNAL OF ALGEBRA 210, 352 360 1998
ARTICLE NO. JA987551
Z .Bounds on Orders of Finite Subgroups of PGL Kn
Eli AljadeffU
and
Jack Sonn
Department of Mathematics, TechnionIsrael Institute of Technology, Haifa, Israel
Communicated by Walter Feit
Received March 15, 1998
Z .We characterize the pairs K, n , K a field, n a positive integer, for which there
Z .is a bound on the orders of finite subgroups of PGL K . Explicit bounds are givenn
in important cases. An application is made to the analogous problem for central
simple Kalgebras of degree n. 1998 Academic Press
1. INTRODUCTION
Z .Let K be a field, n an integer ) 1, GL K the group of invertiblen
Z . Z . U
n = n matrices over K, PGL K s GL K rK . Is there a bound on then n
Z . Z .orders of the finite subgroups of GL K ? of PGL K ? Obviously then n
answer depends on K, because the answer is no if K contains infinitely
many roots of unity. The answer is also no if K is an infinite field of
