Core-free and permutable implies subdirect product of finite nilpotent groups

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Suppose H is a Core-free permutable subgroup (?) of a group G. Then, H is isomorphic to a Subdirect product (?) of Finite nilpotent group (?)s.

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Textbook references

  • Subnormal subgroups of groups by John C. Lennox and Stewart E. Stonehewer, Oxford Mathematical Monographs, ISBN 019853552X, Page 217, Theorem 7.1.10(a), More info