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The tensor product and the 2nd nilpotent product of groups.

Trueman MacHenry — 1960

Mathematische Zeitschrift

On absolutely-nilpotent of class $k$ groups

Patrizia Longobardi; Trueman MacHenry; Mercede Maj; James Wiegold — 1995

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A group $G$ in a variety $V$ is said to be absolutely- $V$ , and we write $G \in A V$ , if central extensions by $G$ are again in $V$ . Absolutely-abelian groups have been classified by F. R. Beyl. In this paper we concentrate upon the class $A N_{k}$ of absolutely-nilpotent of class $k$ groups. We prove some closure properties of the class $A N_{k}$ and we show that every nilpotent of class $k$ group can be embedded in an $A N_{k}$ -gvoup. We describe all metacyclic $A N_{k}$ -groups and we characterize $2$ -generator and infinite $3$ -generator $A N_{2}$ -groups. Finally...

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The tensor product and the 2nd nilpotent product of groups.

On absolutely-nilpotent of class k groups

On absolutely-nilpotent of class $k$ groups