Mat. Zametki:
Mat. Zametki, 2020,	Volume 108,	Issue 2,	Pages 163–170	(Mi mz12671)
This article is cited in 1 scientific paper (total in 1 paper)
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
First page: PDF file
Mathematical Notes, 2020, 108:2, 149–154
Bibliographic databases:
UDC: 512
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
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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