Further solvable analogues of the Baer-Suzuki theorem and generation of\n nonsolvable groups

2010/12/11 by Simon D. Guest, Guest, Simon · 1 citation
Engineering · Mathematics · #20D25 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1012.2480

openalex publication_date 2010/12/11 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

Let G be an almost simple group. We prove that if x \∈ G has prime order\np \≥ 5, then there exists an involution y such that <x,y> is not\nsolvable. Also, if x is an involution then there exist three conjugates of\nx that generate a nonsolvable group, unless x belongs to a short list of\nexceptions, which are described explicitly. We also prove that if x has order\n6 or 9, then there exists two conjugates that generate a nonsolvable group.\n

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