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On absolutely-nilpotent of class k groups

Patrizia Longobardi, Trueman MacHenry, Mercede Maj, James Wiegold (1995)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A group G in a variety V is said to be absolutely- V , and we write G A V , if central extensions by G are again in V . Absolutely-abelian groups have been classified by F. R. Beyl. In this paper we concentrate upon the class A N k of absolutely-nilpotent of class k groups. We prove some closure properties of the class A N k and we show that every nilpotent of class k group can be embedded in an A N k -gvoup. We describe all metacyclic A N k -groups and we characterize 2 -generator and infinite 3 -generator A N 2 -groups. Finally...

On centrally nilpotent loops

L. V. Safonova, K. K. Shchukin (2000)

Commentationes Mathematicae Universitatis Carolinae

Using a lemma on subnormal subgroups, the problem of nilpotency of multiplication groups and inner permutation groups of centrally nilpotent loops is discussed.

On finite abelian groups realizable as Mislin genera.

Peter Hilton, Dirk Scevenels (1997)

Publicacions Matemàtiques

We study the realizability of finite abelian groups as Mislin genera of finitely generated nilpotent groups with finite commutator subgroup. In particular, we give criteria to decide whether a finite abelian group is realizable as the Mislin genus of a direct product of nilpotent groups of a certain specified type. In the case of a positive answer, we also give an effective way of realizing that abelian group as a genus. Further, we obtain some non-realizability results.

On induced morphism of Mislin genera.

Peter Hilton (1994)

Publicacions Matemàtiques

Let N be a nilpotent group with torsion subgroup TN, and let α: TN → T' be a surjective homomorphism such that kerα is normal in N. Then α determines a nilpotent group Ñ such that TÑ = T' and a function α* from the Mislin genus of N to that of Ñ in N (and hence Ñ) is finitely generated. The association α → α* satisfies the usual functiorial conditions. Moreover [N,N] is finite if and only if [Ñ,Ñ] is finite and α* is then a homomorphism of abelian groups. If Ñ belongs to the special class studied...

On locally finite groups and the centralizers of automorphisms

Pavel Shumyatsky (2001)

Bollettino dell'Unione Matematica Italiana

Sia p un primo, e A un gruppo abeliano elementare di ordine p 2 che agisce sul p -gruppo localmente finito G . Supponiamo che esista un intero positivo m tale che C G a , C G b , , C G b m = 1 per ogni a , b A . In questo articolo si dimostra che G è nilpotente, con classe di nilpotenza limitata da una funzione che dipende solo da p e m .

On maximal subgroups of minimax groups

Silvana Franciosi, Francesco de Giovanni (1995)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

It is proved that a soluble residually finite minimax group is finite-by-nilpotent if and only if it has only finitely many maximal subgroups which are not normal.

On semiabelian groups.

Kuzennyi, N.F., Subbotin, I.Ya. (2005)

International Journal of Mathematics and Mathematical Sciences

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