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- W2080153586 abstract "The Baer–Suzuki theorem says that if $$p$$ is a prime, $$x$$ is a $$p$$ -element in a finite group $$G$$ and $$langle x, x^g rangle $$ is a $$p$$ -group for all $$g in G$$ , then the normal closure of $$x$$ in $$G$$ is a $$p$$ -group. We consider the case where $$x^g$$ is replaced by $$y^g$$ for some other $$p$$ -element $$y$$ . While the analog of Baer–Suzuki is not true, we show that some variation is. We also answer a closely related question of Pavel Shumyatsky on commutators of conjugacy classes of $$p$$ -elements." @default.
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- W2080153586 date "2014-10-29" @default.
- W2080153586 modified "2023-09-27" @default.
- W2080153586 title "Variations on the Baer–Suzuki theorem" @default.
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- W2080153586 doi "https://doi.org/10.1007/s00209-014-1399-y" @default.
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