DOCUMENTA MATHEMATICA, Extra Volume ICM II (1998), 67-75

Sergei V. Ivanov

Title: On the Burnside Problem for Groups of Even Exponent

The Burnside problem about periodic groups asks whether any finitely generated group with the law $x^n \equiv 1$ is necessarily finite. This is proven only for $n \leq 4$ and $n=6$. A negative solution to the Burnside problem for odd $n \gg 1$ was given by Novikov and Adian. The article presents a discussion of a recent solution of the Burnside problem for even exponents $n \gg 1$ and related results.

1991 Mathematics Subject Classification: Primary 20F05, 20F06, 20F10, 20F50

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