Nilpotent group - Open Access .click

Journal of the Australian Mathematical Society, 2016
The main purpose of this paper is to investigate the behaviour of uncountable groups of cardinality $\aleph$ in which all proper subgroups of cardinality $\aleph$ are nilpotent. It is proved that such a group $G$ is nilpotent, provided that $G$ has no infinite simple homomorphic images and either $\aleph$ has cofinality strictly larger than $\aleph _{0}
De Giovanni, Francesco, Trombetti, Marco
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Automorphism Groups of Nilpotent Groups

Bulletin of the London Mathematical Society, 1989
Let ${\mathfrak X}$ denote the class of all finitely generated torsion-free nilpotent groups G such that the derived factor group G/G' is torsion- free. For G in ${\mathfrak X}$, let Aut *(G) denote the group of automorphisms of G/G' induced by the automorphism group of G. If G/G' has rank n and we choose a ${\mathbb{Z}}$-basis for G/G' then Aut *
Bryant, R. M., Papistas, A.
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Nilpotent Groups

1994
Abstract With the general theory of the previous chapter in hand, we can begin the structural analysis of groups of finite Morley rank. The general theory occupies Chapters 6 through 9. The present chapter deals with the structure theory for nilpotent groups.
Alexandre Borovik, Ali Nesin
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On constructive nilpotent groups

Siberian Mathematical Journal, 2007
Summary: We prove the following: (1) a torsion-free class 2 nilpotent group is constructivizable if and only if it is isomorphic to the extension of some constructive Abelian group included in the center of the group by some constructive torsion-free Abelian group and some recursive system of factors; (2) a constructivizable torsion-free class 2 ...
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nilpotent groups
fos: mathematics
mathematics - group theory

group theory math.gr
mathematics
finite nilpotent groups, \ p\ -groups

subgroup theorems subgroup growth
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