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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Automorphism groups of nilpotent groups [PDF]

Archiv der Mathematik, 2003
\textit{M. Dugas} and \textit{R. Göbel} [Arch. Math. 54, No. 4, 340-351 (1990: Zbl 0703.20033)] proved the following result: if $H$ is any group, there is a torsion-free nilpotent group $G$ of class $2$ such that $\Aut(G)=H\ltimes\text{Stab}(G)$, where $\text{Stab}(G)$ is the stability group of the series $1\triangleleft Z(G)\triangleleft G$
Rüdiger Göbel, Gábor Braun
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On the nilpotent multipliers of a group

Mathematische Zeitschrift, 1997
Let $G$ be a group presented as a quotient of a free group $F$ by a normal subgroup $R$. The abelian group $M^{(c)}(G)=(R\cap\gamma_{c+1}F)/\gamma_{c+1}(R,F)$ ($c\geq 1$) where $\gamma_1F=F$, $\gamma_{c+1}F=[\gamma_cF,F]$, $\gamma_1(R,F)=R$, $\gamma_{c+1}(R,F)=[\gamma_c(R,F),F]$ is called the $c$-nilpotent multiplier of $G$.
Graham Ellis, John M. Burns
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pure mathematics
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group periodic table

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nilpotent groups

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