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Mat. Zametki, 2020, Volume 108, Issue 2, Pages 163–170 (Mi mz12671)  

This article is cited in 2 scientific papers (total in 2 papers)

Normal Automorphisms of Free Groups of Infinitely Based Varieties

S. I. Adiana, V. S. Atabekyanb

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Yerevan State University

Abstract: In the paper, automorphisms are studied for free groups of varieties given by a family of identities in the well-known infinite independent system of identities involving two variables that was constructed by S. I. Adian to solve the finite basis problem in group theory. It is proved that every normal automorphism (i.e., an automorphism that stabilizes any normal subgroup) of noncyclic free groups of these varieties is an inner automorphism.

Keywords: normal automorphism, variety of groups, simple group, free Burnside group.

Funding Agency Grant Number
State Committee on Science of the Ministry of Education and Science of the Republic of Armenia 10-3/1-41
18T-1A306
The research was partially supported by the State Committee of Science of the Ministry of Education and Science of the Republic of Armenia, grants nos. 10-3/1-41 and 18T-1A306.


DOI: https://doi.org/10.4213/mzm12671

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English version:
Mathematical Notes, 2020, 108:2, 149–154

Bibliographic databases:

UDC: 512
Received: 19.01.2020

Citation: S. I. Adian, V. S. Atabekyan, “Normal Automorphisms of Free Groups of Infinitely Based Varieties”, Mat. Zametki, 108:2 (2020), 163–170; Math. Notes, 108:2 (2020), 149–154

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. S. Atabekyan, “The set of $2$-genereted $C^*$-simple relatively free groups has the cardinality of the continuum”, Uch. zapiski EGU, ser. Fizika i Matematika, 54:2 (2020), 81–86  mathnet  crossref
    2. V. S. Atabekyan, L. D. Beklemishev, V. S. Guba, I. G. Lysenok, A. A. Razborov, A. L. Semenov, “Questions in algebra and mathematical logic. Scientific heritage of S. I. Adian”, Russian Math. Surveys, 76:1 (2021), 1–27  mathnet  crossref  crossref  mathscinet  isi  elib
  • Математические заметки Mathematical Notes
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