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18.84 (2014)

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Let $\pi$ be a set of primes. We say that a finite group is a $\text{BS}_\pi$-group if every conjugacy class in this group any two elements of which generate a $\pi$-subgroup itself generates a $\pi$-subgroup. Is every normal subgroup of a $\text{BS}_\pi$-group a $\text{BS}_\pi$-group?

Contributor: D. O. Revin

Progress

In the case $2 \notin \pi$, an affirmative answer follows from (D. O. Revin, Siberian Math. J., 52, no. 2 (2011), 340–347).

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