On some questions related to integrable groups

2022/07/07 by Russell D. Blyth, Blyth, Russell, Francesco Fumagalli +3 · 1 citation
Mathematics · #20D06 #20D99 #20E28 #20F14 #20G40 #20G41 #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2207.03259

openalex publication_date 2022/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A group G is integrable if it is isomorphic to the derived subgroup of a group H; that is, if H'≃ G, and in this case H is an integral of G. If G is a subgroup of U, we say that G is integrable within U if G=H' for some H≤ U. In this work we focus on two problems posed in [1]. We classify the almost-simple finite groups G that are integrable, which we show to be equivalent to those integrable within Aut(S), where S is the socle of G. We then classify all 2-homogeneous subgroups of the finite symmetric group S_n that are integrable within S_n.

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