zbMATH — the first resource for mathematics

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 \(\operatorname{Aut}\,\mathfrak B(m,n)\).

20F28 Automorphism groups of groups
20F50 Periodic groups; locally finite groups
20M05 Free semigroups, generators and relations, word problems
20E36 Automorphisms of infinite groups
Full Text: DOI
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.