Recognizing the Automorphism Groups of Mathieu Groups Through Their Orders and Large Degrees of Their Irreducible Characters＊

Itisawell-knownfactthatcharactersofafinitegroupcangiveimportantinformationaboutthestructureofthegroup.Itwasalsoprovedbythethirdauthorthatafinitesimplegroupcanbeuniquelydeterminedbyitscharactertable.Heretheauthorsattempttoinvestigatehowtocharacterizeafinitealmost-simplegroupbyusinglessinformationofitscharactertable,andsuccessfullycharacterizetheautomorphismgroupsofMathieugroupsbytheirordersandatmosttwoirreduciblecharacterdegreesoftheircharactertables.