Sui gruppi con molti sottogruppi subnormali
Modularità nei gruppi non-periodici
In questo lavoro sono contenuti alcuni risultati riguardanti la struttura dei gruppi non-periodici in cui sottogruppi verificano opportune condizioni di modularità.
Groups with many nearly normal subgroups
Un sottogruppo di un gruppo si dice nearly normal se ha indice finito nella sua chiusura normale . In questa nota si caratterizzano i gruppi in cui ogni sottogruppo che non sia nearly normal soddisfa una fissata condizione finitaria per diverse scelte naturali della proprietà .
Some lattice properties of normal-by-finite subgroups
A subgroup of a group is said to be normal-by-finite if the core of in has finite index in . It has been proved by Buckley, Lennox, Neumann, Smith and Wiegold that if every subgroup of a group G is normal-by-finite, then is abelian-by-finite, provided that all its periodic homomorphic images are locally finite. The aim of this article is to describe the structure of groups G for which the partially ordered set consisting of all normal-by-finite subgroups satisfies certain relevant...
Groups with complete lattice of nearly normal subgroups.
A subgroup H of a group G is said to be nearly normal in G if it has finite index in its normal closure in G. A well-known theorem of B.H. Neumann states that every subgroup of a group G is nearly normal if and only if the commutator subgroup G' is finite. In this article, groups in which the intersection and the join of each system of nearly normal subgroups are likewise nearly normal are considered, and some sufficient conditions for such groups to be finite-by-abelian are given.
Groups with finitely many conjugacy classes of non-normal subgroups of infinite rank
It is proved that if a locally soluble group of infinite rank has only finitely many non-trivial conjugacy classes of subgroups of infinite rank, then all its subgroups are normal.
Groups with Normality Conditions for Non-Periodic Subgroups
The structure of (non-periodic) groups in which all non-periodic subgroups have a prescribed property is investigated. Among other choices, we consider properties generalizing normality, like subnormality, permutability and pronormality. Moreover, non-periodic groups whose proper non-periodic subgroups belong to a given group class are studied.
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