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arXiv · 2010.05374

The generating pairs of the 2-transitive groups

Junyao Pan
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Abstract

Given a finite group $G$. The generating pair $(H,a)$ of $G$, that is, $H<G$ and $a\in G$ such that $\langle a,H\rangle=G$. In this paper, we introduce the definition of FF-subgroup to characterize the generating pairs of the symmetric groups, alternating groups and projective groups $PSL(2,q)$. This gives a partial answer to an open problem of J. Andr\'e and J. Ara\'ujo and P. J. Cameron.

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Junyao Pan. 2020-10-12. The generating pairs of the 2-transitive groups. https://arxiv.org/abs/2010.05374

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