It is shown that a Carter subgroup of a non-soluble unitary group can only be the normalizer of a Sylow 2-subgroup. This result, combined with previous results, implies that no finite simple group can be a minimal counterexample to the conjugacy conjecture of Carter subgroups in a finite group.
Previtali, A., Tamburini, M., Vdovin, E. (2004). The Carter subgroups of some classical groups. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 36(2), 145-155 [10.1112/S0024609303002558].
The Carter subgroups of some classical groups
PREVITALI, ANDREA;
2004
Abstract
It is shown that a Carter subgroup of a non-soluble unitary group can only be the normalizer of a Sylow 2-subgroup. This result, combined with previous results, implies that no finite simple group can be a minimal counterexample to the conjugacy conjecture of Carter subgroups in a finite group.
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