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arXiv · 2509.17330

Some new compatible groups

Zhaochen Ding·Gabriel Verret
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Abstract

Two finite groups $L_1$ and $L_2$ are compatible if there exists a finite group $G$ with isomorphic normal subgroups $N_1$ and $N_2$ such that $L_1\cong G/N_1$ and $L_2\cong G/N_2$. 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.

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Zhaochen Ding, Gabriel Verret. 2025-09-22. Some new compatible groups. https://arxiv.org/abs/2509.17330

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