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4.74 (1973)

Partially Solved

a) Is every 2-group of order greater than 2 non-simple?
b) Is every binary-finite 2-group of order greater than 2 non-simple?

Contributor: V. P. Shunkov

Progress

a) No, the existence of simple infinite 2-groups follows from the existence of finitely generated infinite groups of exponent $2^n$ (S. V. Ivanov, Int. J. Algebra Comput., 4, no. 1–2 (1994), 1–308; I. G. Lysënok, Izv. Math., 60, no. 3 (1996), 453–654) and from the positive solution to the Restricted Burnside Problem for groups of exponent $2^n$ (E. I. Zel’manov, Math. USSR–Sb., 72 (1992), 543–565).

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