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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 \(n\), \(n\geq 1039\).

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
Full Text: DOI
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