Artinian and noetherian factorized groups
Bernhard Amberg (1976)
Rendiconti del Seminario Matematico della Università di Padova
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Bernhard Amberg (1976)
Rendiconti del Seminario Matematico della Università di Padova
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Patrizia Longobardi, Mercede Maj, Avinoam Mann, Akbar Rhemtulla (1996)
Rendiconti del Seminario Matematico della Università di Padova
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Howard Smith (2011)
Rendiconti del Seminario Matematico della Università di Padova
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Bernhard Amberg (1983)
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.
Bertram Wehrfritz (2011)
Open Mathematics
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Let ϕ be an automorphism of prime order p of the group G with C G(ϕ) finite of order n. We prove the following. If G is soluble of finite rank, then G has a nilpotent characteristic subgroup of finite index and class bounded in terms of p only. If G is a group with finite Hirsch number h, then G has a soluble characteristic subgroup of finite index in G with derived length bounded in terms of p and n only and a soluble characteristic subgroup of finite index in G whose index and derived...
Javier Otal, Juan Manuel Peña (1991)
Rendiconti del Seminario Matematico della Università di Padova
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Artemovych, O. (2002)
Serdica Mathematical Journal
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We characterize the groups which do not have non-trivial perfect sections and such that any strictly descending chain of non-“nilpotent-by-finite” subgroups is finite.
Enrico Jabara (2006)
Matematički Vesnik
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James C. Beidleman, Howard Smith (1993)
Rendiconti del Seminario Matematico della Università di Padova
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