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On some properties of pronormal subgroups

Leonid Kurdachenko, Alexsandr Pypka, Igor Subbotin (2010)

Open Mathematics

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.

On some soluble groups in which U -subgroups form a lattice

Leonid A. Kurdachenko, Igor Ya. Subbotin (2007)

Commentationes Mathematicae Universitatis Carolinae

The article is dedicated to groups in which the set of abnormal and normal subgroups ( U -subgroups) forms a lattice. A complete description of these groups under the additional restriction that every counternormal subgroup is abnormal is obtained.

On some subgroup chains related to Kneser’s theorem

Yahya Ould Hamidoune, Oriol Serra, Gilles Zémor (2008)

Journal de Théorie des Nombres de Bordeaux

A recent result of Balandraud shows that for every subset S of an abelian group G there exists a non trivial subgroup H such that | T S | | T | + | S | - 2 holds only if H S t a b ( T S ) . Notice that Kneser’s Theorem only gives { 1 } S t a b ( T S ) .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...

On special p -groups

Renza Cortini (1998)

Bollettino dell'Unione Matematica Italiana

In questo lavoro viene data una caratterizzazione di quei p -gruppi nilpotenti di classe due ed esponente p che sono speciali. Vengono inoltre studiate alcune costruzioni, automorfismi e sottogruppi abeliani di p -gruppi speciali.

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