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On automorphisms and embeddings of free periodic groups. (English. Russian original) Zbl 1299.20057
J. Contemp. Math. Anal., Armen. Acad. Sci. 46, No. 2, 106-112 (2011); translation from Izv. Nats. Akad. Nauk Armen., Mat. 46, No. 2, 59-70 (2011).
Summary: The paper gives a construction of a free monoid of rank 2 in the group of automorphisms of free periodic groups \(B(m,n)\) of any odd period \(n\geq 665\) and any rank \(m>1\). Moreover, it is proved that if the period is any prime number \(n>1003\) and the group \(B(m,n)\) is nested in some \(n\)-periodic group \(G\) as a normal subgroup, then \(B(m,n)\) is a direct factor in \(G\).
MSC:
20F50 Periodic groups; locally finite groups
20F05 Generators, relations, and presentations of groups
20F28 Automorphism groups of groups
20M05 Free semigroups, generators and relations, word problems
20E07 Subgroup theorems; subgroup growth
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References:
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