All automorphisms of the 3-nilpotent free group of countably infinite rank can be lifted

Piotr Włodzimierz Gawron; Olga Macedońska

doi:10.1016/0021-8693(88)90052-X

All automorphisms of the 3-nilpotent free group of countably infinite rank can be lifted

Piotr Włodzimierz Gawron
, Olga Macedońska

Department of Mathematics (RMS/RMS1)

Silesian University of Technology

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

It is known from S. Andreadakis (Proc. London Math. Soc. (3) 15 (1965), 239-268) and S. Bachmuth (Trans. Amer. Math. Soc. 122 (1966), 1-17) that for a free 3-nilpotent group F ̄ of rank n the map Aut F → Aut F ̄ is not onto. It is proved here that for F countably infinitely generated the map is onto.

Original language	English
Pages (from-to)	120-128
Number of pages	9
Journal	Journal of Algebra
Volume	118
Issue number	1
DOIs	https://doi.org/10.1016/0021-8693(88)90052-X
Publication status	Published - Oct 1988

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/0021-8693(88)90052-X

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title = "All automorphisms of the 3-nilpotent free group of countably infinite rank can be lifted",

abstract = "It is known from S. Andreadakis (Proc. London Math. Soc. (3) 15 (1965), 239-268) and S. Bachmuth (Trans. Amer. Math. Soc. 122 (1966), 1-17) that for a free 3-nilpotent group F{\= } of rank n the map Aut F → Aut F{\= } is not onto. It is proved here that for F countably infinitely generated the map is onto.",

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N2 - It is known from S. Andreadakis (Proc. London Math. Soc. (3) 15 (1965), 239-268) and S. Bachmuth (Trans. Amer. Math. Soc. 122 (1966), 1-17) that for a free 3-nilpotent group F ̄ of rank n the map Aut F → Aut F ̄ is not onto. It is proved here that for F countably infinitely generated the map is onto.

AB - It is known from S. Andreadakis (Proc. London Math. Soc. (3) 15 (1965), 239-268) and S. Bachmuth (Trans. Amer. Math. Soc. 122 (1966), 1-17) that for a free 3-nilpotent group F ̄ of rank n the map Aut F → Aut F ̄ is not onto. It is proved here that for F countably infinitely generated the map is onto.

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U2 - 10.1016/0021-8693(88)90052-X

DO - 10.1016/0021-8693(88)90052-X

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All automorphisms of the 3-nilpotent free group of countably infinite rank can be lifted

Abstract

ASJC Scopus subject areas

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