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.

中文翻译：

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基于无穷大的自由群的正规自同构

本文研究了著名的无限独立恒等式系统中由一族恒等式给出的自由变体群的自同构，该系统涉及两个变量，SI Adian 为解决群论中的有限基问题而构造。证明了这些变体的非循环自由群的每一个正规自同构（即稳定任何正规子群的自同构）都是一个内自同构。