Some new compatible groups

2025/09/22 by Ding, Zhaochen, Gabriel Verret, Verret, Gabriel
Mathematics · #20D99 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2509.17330

openalex publication_date 2025/09/22 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

Two finite groups L₁ and L₂ are compatible if there exists a finite group G with isomorphic normal subgroups N₁ and N₂ such that L₁≅ G/N₁ and L₂≅ G/N₂. We prove a new sufficient condition for two groups to be compatible. As a corollary, we obtain that nilpotent groups of the same order are compatible, and so are groups of the same square-free order.

Citations

• Some necessary conditions for compatibility of groups
• Arc-transitive digraphs with quasiprimitive local actions

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• One formation of finite groups
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