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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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