Abstract
In this chapter we discuss some instances of the Burnside Problem. There are three versions of this problem, the first one being the ``General Burnside Problem: Is it true that if a group G is finitely generated and torsion, then it is finite?’’ We discuss the General Burnside problem for locally finite groups (Section 6.2), for polycyclic-by-finite and solvable groups (Section 6.3), as well as its bounded version for linear groups (Section 6.4). Finally, in Section 6.5 we discuss the Kurosh–Levitzky problem (on nil algebras) and explain the construction of Golod and Shafarevich yielding a negative answer to the Kurosh–Levitzky problem and therefore to the General Burnside Problem.
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Ceccherini-Silberstein, T., D’Adderio, M. (2021). The Burnside Problem. In: Topics in Groups and Geometry. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-88109-2_6
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DOI: https://doi.org/10.1007/978-3-030-88109-2_6
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