subgroup

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1) The hypotheses are inherited by all proper subgroups, thus G is a group which is not p-nilpotent but whose proper subgroups are all p-nilpotent.
Thus K, K [intersection] N satisfy the hypotheses of the theorem in any case, so K is p-nilpotent, therefore G is a group which is not p-nilpotent but whose proper subgroups are all p-nilpotent.
p'] since that G is a group which is not nilpotent but whose proper subgroups are all nilpotent.

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