Displaying similar documents to “Groups with finite conjugacy classes of subnormal subgroups”

Groups with many nearly normal subgroups

Maria De Falco (2001)

Bollettino dell'Unione Matematica Italiana

Similarity:

Un sottogruppo H di un gruppo G si dice nearly normal se ha indice finito nella sua chiusura normale H G . In questa nota si caratterizzano i gruppi in cui ogni sottogruppo che non sia nearly normal soddisfa una fissata condizione finitaria χ per diverse scelte naturali della proprietà χ .

Groups with small deviation for non-subnormal subgroups

Leonid Kurdachenko, Howard Smith (2009)

Open Mathematics

Similarity:

We introduce the notion of the non-subnormal deviation of a group G. If the deviation is 0 then G satisfies the minimal condition for nonsubnormal subgroups, while if the deviation is at most 1 then G satisfies the so-called weak minimal condition for such subgroups (though the converse does not hold). Here we present some results on groups G that are either soluble or locally nilpotent and that have deviation at most 1. For example, a torsion-free locally nilpotent with deviation at...

The nilpotency of some groups with all subgroups subnormal.

Leonid A. Kurdachenko, Howard Smith (1998)

Publicacions Matemàtiques

Similarity:

Let G be a group with all subgroups subnormal. A normal subgroup N of G is said to be G-minimax if it has a finite G-invariant series whose factors are abelian and satisfy either max-G or min- G. It is proved that if the normal closure of every element of G is G-minimax then G is nilpotent and the normal closure of every element is minimax. Further results of this type are also obtained.