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Non-$$\varphi$$-admissible normal subgroups of free Burnside groups. (English. Russian original) Zbl 1299.20046
J. Contemp. Math. Anal., Armen. Acad. Sci. 45, No. 2, 112-122 (2010); translation from Izv. Nats. Akad. Nauk Armen., Mat. 45, No. 2, 21-36 (2010).
Summary: In the present paper for an arbitrary automorphism $$\varphi$$ of the free Bunside group $$B(m,n)$$ and for any odd number $$n\geq 1003$$ a sufficient condition for existence of a non-$$\varphi$$-admissible normal subgroup of $$B(m,n)$$ is found. In particular, if automorphism $$\varphi$$ is normal, then for any basis $$\{a_1,a_2,\ldots,a_m\}$$ of the group $$B(m,n)$$ there is an integer $$k$$ such that for each $$i$$ the elements $$a_i$$ and $$\varphi(a_i)^k$$ are conjugate.

##### MSC:
 20E36 Automorphisms of infinite groups 20F50 Periodic groups; locally finite groups 20F05 Generators, relations, and presentations of groups
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##### References:
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