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Groups with every subgroup ascendant-by-finite
Cent. Eur. J. Math., 11(12), 2182-2185 (2013)
Abstract: A subgroup H of a group G is called ascendant-by-finite in G if there exists a subgroup K of H such that K is ascendant in G and the index of K in H is finite. It is proved that a locally finite group with every subgroup ascendant-by-finite is locally nilpotent-by-finite. As a consequence, it is shown that the Gruenberg radical has finite index in the whole group.
MSC: 20F19, 20F22, 20F50
Keywords: Ascendant subgroup, Locally nilpotent, Radical, Locally finite group