On the Pronormality of Subgroups of Odd Index in Finite Simple Groups

2018/07/01 by А. С. Кондратьев, Kondrat'ev, Anatoly S., Н. В. Маслова +3
Computer Science · Engineering · Mathematics · #20D06 #20D60 #Advanced Graph Theory Research #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1807.00384

openalex publication_date 2018/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A subgroup H of a group G is said to be pronormal in G if H and H^g are conjugate in ⟨ H, H^g ⟩ for every g ∈ G. Some problems in finite group theory, combinatorics, and permutation group theory were solved in terms of pronormality. In 2012, E. Vdovin and the third author conjectured that the subgroups of odd index are pronormal in finite simple groups. In this paper we disprove their conjecture and discuss a recent progress in the classification of finite simple groups in which the subgroups of odd index are pronormal.

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