On some problems of Petrich concerning Brück and Reilly semigroups.
New results on tight connections among pronormal, abnormal and contranormal subgroups of a group have been established. In particular, new characteristics of pronormal and abnormal subgroups have been obtained.
The article is dedicated to groups in which the set of abnormal and normal subgroups (-subgroups) forms a lattice. A complete description of these groups under the additional restriction that every counternormal subgroup is abnormal is obtained.
A recent result of Balandraud shows that for every subset of an abelian group there exists a non trivial subgroup such that holds only if . Notice that Kneser’s Theorem only gives .This strong form of Kneser’s theorem follows from some nice properties of a certain poset investigated by Balandraud. We consider an analogous poset for nonabelian groups and, by using classical tools from Additive Number Theory, extend some of the above results. In particular we obtain short proofs of Balandraud’s...
In questo lavoro viene data una caratterizzazione di quei -gruppi nilpotenti di classe due ed esponente che sono speciali. Vengono inoltre studiate alcune costruzioni, automorfismi e sottogruppi abeliani di -gruppi speciali.