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Monomorphisms of free Burnside groups. (English. Russian original) Zbl 1200.20028
Math. Notes 86, No. 4, 457-462 (2009); translation from Mat. Zametki 86, No. 4, 483-490 (2009).
Summary: It is proved that, for any odd \(n\geq 1039\), there are words \(u(x,y)\) and \(v(x,y)\) over the group alphabet \(\{x,y\}\) such that, if \(a\) and \(b\) are any two noncommuting elements of the free Burnside group \(B(m,n)\), then, for some \(k\), the elements \(u(a^k,b)\) and \(v(a^k,b)\) freely generate a free Burnside subgroup of the group \(B(m,n)\). In particular, the facts proved in the paper imply the uniform nonamenability of the group \(B(m,n)\) for odd \(n\), \(n\geq 1039\).

MSC:
20F50 Periodic groups; locally finite groups
20F05 Generators, relations, and presentations of groups
20E07 Subgroup theorems; subgroup growth
20E36 Automorphisms of infinite groups
43A07 Means on groups, semigroups, etc.; amenable groups
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