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.
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Funding
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.
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Adian, S.I., Atabekyan, V.S. Normal Automorphisms of Free Groups of Infinitely Based Varieties. Math Notes 108, 149–154 (2020). https://doi.org/10.1134/S0001434620070159
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DOI: https://doi.org/10.1134/S0001434620070159