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16.64 (2006)

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A non-abelian variety in which all finite groups are abelian is called pseudo-abelian. A group variety is called a $t$-variety if for all groups in this variety the relation of being a normal subgroup is transitive. By (O. Macedońska, A. Storozhev, Commun. Algebra, 25, no. 5 (1997), 1589–1593) each non-abelian $t$-variety is pseudo-abelian, and the pseudo-abelian varieties constructed in (A. Yu. Olshanskii, Math. USSR–Sb., 54 (1986), 57–80) are $t$-varieties. Is every pseudo-abelian variety a $t$-variety?

Contributor: O. Macedońska

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