Automorphisms of the Gersten Group

F. A. Dudkin; E. A. Shaporina

doi:10.1134/S0037446621030046

Automorphisms of the Gersten Group

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Abstract

The Gersten group $ G $ is the split extension (Formula Presented.) of the free group F₃ with basis {a,b,c} bythe automorphism ϕ : a → a, b → ba, c → ca2.We describe the generators and structure of the group Out(G) and prove that(Formula Presented.).

Original language	English
Pages (from-to)	413-422
Number of pages	10
Journal	Siberian Mathematical Journal
Volume	62
Issue number	3
DOIs	https://doi.org/10.1134/S0037446621030046
Publication status	Published - May 2021

Keywords

512.54
automorphism
free group
Gersten group
outer automorphism group

OECD FOS+WOS

1.01 MATHEMATICS

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10.1134/S0037446621030046

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title = "Automorphisms of the Gersten Group",

abstract = "The Gersten group $ G $ is the split extension (Formula Presented.) of the free group F3 with basis {a,b,c} bythe automorphism ϕ : a → a, b → ba, c → ca2.We describe the generators and structure of the group Out(G) and prove that(Formula Presented.).",

keywords = "512.54, automorphism, free group, Gersten group, outer automorphism group",

author = "Dudkin, {F. A.} and Shaporina, {E. A.}",

note = "Funding Information: F. A. Dudkin was supported by the Mathematical Center in Akademgorodok (Agreement No. 075–15–2019–1613 with the Ministry of Science and Higher Education of the Russian Federation). Publisher Copyright: {\textcopyright} 2021, Pleiades Publishing, Ltd.",

year = "2021",

month = may,

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language = "English",

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pages = "413--422",

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AU - Dudkin, F. A.

AU - Shaporina, E. A.

N1 - Funding Information: F. A. Dudkin was supported by the Mathematical Center in Akademgorodok (Agreement No. 075–15–2019–1613 with the Ministry of Science and Higher Education of the Russian Federation). Publisher Copyright: © 2021, Pleiades Publishing, Ltd.

PY - 2021/5

Y1 - 2021/5

N2 - The Gersten group $ G $ is the split extension (Formula Presented.) of the free group F3 with basis {a,b,c} bythe automorphism ϕ : a → a, b → ba, c → ca2.We describe the generators and structure of the group Out(G) and prove that(Formula Presented.).

AB - The Gersten group $ G $ is the split extension (Formula Presented.) of the free group F3 with basis {a,b,c} bythe automorphism ϕ : a → a, b → ba, c → ca2.We describe the generators and structure of the group Out(G) and prove that(Formula Presented.).

KW - 512.54

KW - automorphism

KW - free group

KW - Gersten group

KW - outer automorphism group

UR - http://www.scopus.com/inward/record.url?scp=85106934396&partnerID=8YFLogxK

U2 - 10.1134/S0037446621030046

DO - 10.1134/S0037446621030046

M3 - Article

AN - SCOPUS:85106934396

VL - 62

SP - 413

EP - 422

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 3

ER -

Automorphisms of the Gersten Group

Abstract

Keywords

OECD FOS+WOS

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