Abstract
Given a nonempty set ω of primes and a nonempty formation F of finite groups, we define the F ω-normalizer in a finite group and study their properties (existence, invariance under certain homomorphisms, conjugacy, embedding, and so on) in the case that F is an ω-local formation. We so develop the results of Carter, Hawkes, and Shemetkov on the F-normalizers in groups.
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In memory of Professor Leonid Aleksandrovich Shemetkov (on the occasion of the 80th anniversary of his birth).
Moscow; Bryansk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 58, No. 1, pp. 64–82, January–February, 2017; DOI: 10.17377/smzh.2017.58.107.
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Vedernikov, V.A., Sorokina, M.M. The F ω-normalizers of finite groups. Sib Math J 58, 49–62 (2017). https://doi.org/10.1134/S0037446617010074
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DOI: https://doi.org/10.1134/S0037446617010074