The Burnside problem, posed by William Burnside in 1902 and one of the oldest and most influential questions in group theory, asks whether a finitely generated group in which every element has finite order must necessarily be a finite group. Evgeny Golod and Igor Shafarevich provided a counter-example in 1964. The problem has many variants (see and below) that differ in the additional conditions imposed on the orders of the group elements.