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On group automorphisms fixing subnormal subgroups setwise

Ulderico Dardano, Clara Franchi (2000)

Bollettino dell'Unione Matematica Italiana

In questo lavoro si studiano i gruppi Aut s n G , Aut d G , Aut χ G degli automorfismi di un gruppo G che fissano — come insiemi — tutti i sottogruppi di G che risultano essere rispettivamente subnormali, subnormali di difetto al più d , oppure che sono compresi tra un sottogruppo caratteristico ed il suo derivato. Si danno condizioni sufficienti affinché tali gruppi siano parasolubili di para-altezza al più 2 o 3. Si generalizzano così risultati da [4], [7], [8], [10].

On Groups whose Contranormal Subgroups are Normally Complemented

Kurdachenko, L. A., Subbotin, I. Ya. (2011)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 20F16, 20E15.Groups in which every contranormal subgroup is normally complemented has been considered. The description of such groups G with the condition Max-n and such groups having an abelian nilpotent residual satisfying Min-G have been obtained.

On groups with linear sci growth

Louis Funar, Martha Giannoudovardi, Daniele Ettore Otera (2015)

Fundamenta Mathematicae

We prove that the semistability growth of hyperbolic groups is linear, which implies that hyperbolic groups which are sci (simply connected at infinity) have linear sci growth. Based on the linearity of the end-depth of finitely presented groups we show that the linear sci is preserved under amalgamated products over finitely generated one-ended groups. Eventually one proves that most non-uniform lattices have linear sci.

On groups with property

Olympia Talelli (1988)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

On hypercentral groups

B. Wehrfritz (2007)

Open Mathematics

Let G be a hypercentral group. Our main result here is that if G/G’ is divisible by finite then G itself is divisible by finite. This extends a recent result of Heng, Duan and Chen [2], who prove in a slightly weaker form the special case where G is also a p-group. If G is torsion-free, then G is actually divisible.

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