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We let M be a maximal proper subgroup of G such that A [less than or equal to] M.
Suppose [C.sub.A] and [C.sub.B] are proper subgroups of A and B; respectively.
([1], IV, 5.4) Suppose that G is a group which is not nilpotent but whose proper subgroups are all nilpotent.
Clearly [J.sub.1] and [J.sub.2] are additive proper subgroups of J whose union is J.

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