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Abstract
AbstractA 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 is prosolvable and any quotient of it is again MP. As corollaries, we obtain that a prime divisor of is 2, 3, 5 or 7, and the second derived subgroup of is pronilpotent. We also show that the inverse limit of an inverse system of profinite MP groups is again MP. Finally when is finitely generated, we establish that must in fact be finite.
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