## On Nilpotent Divisible Groups |

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### Contents

Extension and Embedding | 5 |

The Structure of the Free Nilpotent Dgroup | 27 |

Local Nilpotency and Related Concepts | 60 |

1 other sections not shown

### Common terms and phrases

abelian D-group arbitrary element basic symbols Cauchy sequence center of G characteristic subgroup coefficient commutators of degree D-Frattini subgroup D-gp D-group G D-sub D-subgroup containing D-subgroup of G define Definition denote direct product element x e elements of G epimorphism FC-nilpotent finite class finite number finite product finitely D-generated follows formal power series free group free nilpotent D-group G containing G is called group G homomorphism 9 Homomorphism Theorem inductive hypothesis isomorphism kernel of 9 lemma Let G Let H locally nilpotent Locally Nilpotent Groups lower central series map 9 maximal D-subgroup mod G n+l n n=l n nilpotent of class non-zero integers normal subgroup null sequence number of D-generators Proof rational powers sequence of elements subset torsion-free U G(n UD property vector space x e G x e H Zorn's lemma