18 research outputs found
On generations by conjugate elements in almost simple groups with socle \mbox{}^2F_4(q^2)'
We prove that if L=\mbox{}^2F_4(2^{2n+1})' and is a nonidentity
automorphism of then has four elements conjugate to
that generate . This result is used to study the following conjecture
about the -radical of a finite group: Let be a proper subset of the
set of all primes and let be the least prime not belonging to . Set
if or and set if . Supposedly, an element
of a finite group is contained in the -radical
if and only if every conjugates of generate a
-subgroup. Based on the results of this paper and a few previous ones, the
conjecture is confirmed for all finite groups whose every nonabelian
composition factor is isomorphic to a sporadic, alternating, linear, or unitary
simple group, or to one of the groups of type ,
, , , or