ON OVERGROUPS OF E(E_6, R) AND E(E_7, R) IN THEIR MINIMAL REPRESENTATIONS

摘要

Overgroups of elementary Chevalley groups of types E_6 and E_7 in their minimal irreducible representations are dealt with. One of the first steps toward their description, namely, the construction of a series of perfect intermediate groups, is performed. Probably all perfect intermediate groups for groups of type E_6 are described. A conjecture concerning the structure of perfect overgroups of type E_7 is suggested.