IMI/Publicaţii/BASM/Ediţii/BASM n.3 (40), 2002/

nX-Complementary generations of the sporadic group Suz. (English)

Authors: Ashrafi A.R., Moghani G.A.


Let G be a finite group and nX be a conjugacy class of elements of order n in G. G is called (l,m,n)-generated if it is a quotient group of the triangle group T(l,m,n) = { x,y,z | xl = ym = zn = xyz = 1}, and nX-complementary generated if, for any arbitrary x belongs G - {1}, there is a y belongs nX such that G=< x,y >. In [18], the question of finding all positive integers n such that non-abelian finite simple group G is nX-complementary generated was posed. In this paper, we partially answer this question for the Suzuki group Suz. In fact, we prove that for every conjugacy class nX of elements of order n, the sporadic group Suz is nX-complementary generated if and only if nX = 3C or n >= 4 and nX isn't equal 4A, 6A.

A.R. Ashrafi
Department of Mathematics
Faculty of Science
University of Kashan
Kashan, Iran
G.A. Moghani
Department of Mathematics
Faculty of Basic Science
University of Mazandaran
Babolsar, Iran