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

Katedra Matematyki (RMS/RMS1)

Silesian University of Technology

Wyniki badań: Wkład do czasopisma › Artykuł › recenzja

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Abstrakt

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.

Język oryginału	angielski
Strony (od–do)	120-128
Liczba stron	9
Czasopismo	Journal of Algebra
Tom	118
Numer wydania	1
Identyfikatory DOI	https://doi.org/10.1016/0021-8693(88)90052-X
Status publikacji	Opublikowano - paź 1988

Obszary tematyczne ASJC Scopus

Algebra i teoria liczb

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

Abstrakt

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