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.
@article{bwmeta1.element.doi-10_2478_s11533-009-0067-7,
author = {Martyn Dixon and Martin Evans and Antonio Tortora},
title = {On totally inert simple groups},
journal = {Open Mathematics},
volume = {8},
year = {2010},
pages = {22-25},
zbl = {1204.20030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0067-7}
}
Martyn Dixon; Martin Evans; Antonio Tortora. On totally inert simple groups. Open Mathematics, Tome 8 (2010) pp. 22-25. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0067-7/
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