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Free semigroup in the group of automorphisms of the free Burnside group. (English) Zbl 1121.20028
Summary: Let \(\mathfrak B(m,n)\) be a free Burnside group of a sufficiently large exponent \(n\) with a basis of cardinality \(m\), \(m\geq 2\). We prove the existence of a free semigroup of rank 2 in \(\operatorname{Aut}\,\mathfrak B(m,n)\).

MSC:
20F28 Automorphism groups of groups
20F50 Periodic groups; locally finite groups
20M05 Free semigroups, generators and relations, word problems
20E36 Automorphisms of infinite groups
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[1] Adian S. I., The Burnside problem and identities in groups (1979) · doi:10.1007/978-3-642-66932-3
[2] DOI: 10.1142/S0218196794000026 · Zbl 0822.20044 · doi:10.1142/S0218196794000026
[3] Lysionok I. G., Math. Ross. Izv. 60 pp 3– (1996) · doi:10.4213/im77
[4] Novikov P. S., Izv. Acad. Nauk SSSRT, 32, in: On Infinite Periodical Groups I–III (1968)
[5] Ol’shanskii A. Yu., Mat. Sb. 118 pp 203– (1982)
[6] DOI: 10.1007/978-94-011-3618-1 · doi:10.1007/978-94-011-3618-1
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