Abstract
A subgroup H of a group G is inert if |H: H ∩ H g| is finite for all g ∈ G and a group G is totally inert if every subgroup H of G is inert. We investigate the structure of minimal normal subgroups of totally inert groups and show that infinite locally graded simple groups cannot be totally inert.
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Dixon, M.R., Evans, M.J. & Tortora, A. On totally inert simple groups. centr.eur.j.math. 8, 22–25 (2010). https://doi.org/10.2478/s11533-009-0067-7
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DOI: https://doi.org/10.2478/s11533-009-0067-7