The automorphism group of finite p-groups associated to the Macdonald group

2023/03/11 by Alexander Montoya Ocampo, Ocampo, Alexander Montoya, Fernando Szechtman +1
Mathematics · Chemistry · #Finite Group Theory Research #Carbohydrate Chemistry and Synthesis

paper · pdf · doi:10.48550/arxiv.2303.06385

Abstract

Given positive integers p and m, where p is assumed to be an odd prime, we determine the automorphism groups of p-groups J, H, and K of orders p^7m, p^6m, and p^5m, and nilpotency classes 5, 4, and 3, respectively, all of which arise naturally from the Macdonald group ⟨ x,y | x^[x,y]=x^1+pmℓ, y^[y,x]=y^1+pmℓ⟩, where ℓ∈\mathbf Z is relatively prime to p.

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