2024/12/11 by Claude Marion, Marion, Claude, Pavel Zalesskii +1
Mathematics · #Finite Group Theory Research #Geometric and Algebraic Topology #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2412.08470
A group is said to have the Magnus Property (MP) if whenever two elements have the same normal closure then they are conjugate or inverse-conjugate. We show that a profinite MP group G is prosolvable and any quotient of it is again MP. As corollaries we obtain that the only prime divisors of |G| are 2, 3, 5 and 7, and the second derived subgroup of G is pronilpotent. We also show that the inverse limit of an inverse system of profinite MP groups is again MP. Finally when G is finitely generated, we establish that G must in fact be finite.