Subgroups of locally normal groups
B. Hartley (1976)
Compositio Mathematica
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B. Hartley (1976)
Compositio Mathematica
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Brunella Bruno, Richard E. Phillips (1983)
Rendiconti del Seminario Matematico della Università di Padova
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Martyn Dixon, Martin Evans, Antonio Tortora (2010)
Open Mathematics
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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.
Felix Leinen (1986)
Rendiconti del Seminario Matematico della Università di Padova
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Sergio Camp-Mora (2013)
Open Mathematics
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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.
B. Hartley, M. J. Tomkinson (1988)
Rendiconti del Seminario Matematico della Università di Padova
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M. Kuzucuoğlu (1993)
Rendiconti del Seminario Matematico della Università di Padova
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Francesco de Giovanni, Alessio Russo (2002)
Mathematica Slovaca
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