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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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