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If X is a class of groups, a group G is said to be just-non-X if it is not in X but all its proper quotients are X-groups. A description of just-non-(nilpotent-by-finite) groups and just-non-(supersoluble-by-finite) groups is given in this paper. *doi:10.3318/pria.2002.102.2.131 fatcat:o5vxwlb4fzcs5ogbrbtzkvycwq