Normal Automorphisms of Free Groups of Infinitely Based Varieties

S. I. Adian ; V. S. Atabekyan

Matematičeskie zametki, Tome 108 (2020) no. 2, pp. 163-170.

Résumé

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.

Détail

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

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