On <italic>Kn</italic>-simple groups and traces of maximal subgroups.

<bold><italic>Abstract–</italic>In this paper, based on the classifications of <italic>Kn</italic>-simple groups for</bold> n≤6 <bold>and under the case that every maximal subgroup has a <italic>π</italic>-nilpotent trace, we obtained the necessary and sufficient conditions on solvable groups and proved that two unsolvable problems involving groups, rings and fields are true.</bold> [ABSTRACT FROM AUTHOR]