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4.73 (1973)

Solved

(Well-known problem). Does there exist a non-abelian variety of groups
$\qquad$ a) all of whose finite groups are abelian?
$\qquad$ b) all of whose periodic groups are abelian?

Contributor: A. L. Shmel’kin

Progress

a) Yes, there does (A. Yu. Olshanskii, Math. USSR–Sb., 54 (1986), 57–80).
b) Yes, there does (P. A. Kozhevnikov, On varieties of groups of large odd exponent, Dep. 1612-V00, VINITI, Moscow, 2000 (Russian); S. V. Ivanov, A. M. Storozhev, Contemp. Math., 360 (2004), 55–62).

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