Groups with every subgroup ascendant-by-finite

• Autorzy: Sergio Camp-Mora
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Ascendant subgroup; Locally nilpotent; Radical; Locally finite group

Kategorie tematyczne

• 20F50: Periodic groups; locally finite groups
• 20F22: Other classes of groups defined by subgroup chains
• 20F19: Generalizations of solvable and nilpotent groups

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 12
• Strony: 2182-2185

Daty

wydano

2013-12-01

online

2013-10-08

Twórcy

autor

Sergio Camp-Mora

• Universidad Politécnica de Valencia

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0312-y