Abstract
Let A be an abelian subgroup of a finite group G, and let B be a nilpotent subgroup of G. If G is solvable, then we prove that it contains an element g such that A ∩ B g ≤ F(G), where F(G) is the Fitting subgroup of G. If G is not solvable, we prove that a counterexample of minimal order to the conjecture that A ∩ B g ≤ F(G) for some element g from G is an almost simple group.
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References
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Original Russian Text © V.I. Zenkov, 2015, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Vol. 21, No. 3.
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Zenkov, V.I. On intersections of abelian and nilpotent subgroups in finite groups. I. Proc. Steklov Inst. Math. 295 (Suppl 1), 174–177 (2016). https://doi.org/10.1134/S0081543816090182
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DOI: https://doi.org/10.1134/S0081543816090182