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arXiv · 2203.02705

Counterexamples to a conjecture of M. Pellegrini and P. Shumyatsky

Rijubrata Kundu·Sumit Chandra Mishra
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Abstract

In this article, we provide counterexamples to a conjecture of M. Pellegrini and P. Shumyatsky which states that each coset of the centralizer of an involution in a finite non-abelian simple group $G$ contains an odd order element, unless $G=\text{PSL}(n,2)$ for $n\geq 4$. More precisely, we show that the conjecture does not hold for the alternating group $A_{8n}$ for all $n\geq 2$.

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Rijubrata Kundu, Sumit Chandra Mishra. 2022-03-05. Counterexamples to a conjecture of M. Pellegrini and P. Shumyatsky. https://doi.org/10.1007/s11587-022-00748-8

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