Abstract
Overgroups of elementary Chevalley groups of types E6 and E7 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 E6 are described. A conjecture concerning the structure of perfect overgroups of type E7 is suggested. Bibliography: 23 titles.
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