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Locally finite groups with all subgroups either subnormal or nilpotent-by-Chernikov

Open Mathematics, 2012
Abstract Let G be a locally finite group satisfying the condition given in the title and suppose that G is not nilpotent-by-Chernikov. It is shown that G has a section S that is not nilpotent-by-Chernikov, where S is either a p-group or a semi-direct product of the additive group A of a locally finite field F by a subgroup K of the ...
Giovanni Cutolo, Smith Howard
exaly   +11 more sources

Locally finite p-groups with all subgroups either subnormal or nilpotent-by-Chernikov [PDF]

International Journal of Group Theory, 2012
We pursue further our investigation, begun in [H.~Smith, Groups with all subgroups subnormal or nilpotent-by-{C}hernikov, emph{Rend. Sem. Mat. Univ. Padova} 126 (2011), 245--253] and continued in [G.~Cutolo and H.~Smith, Locally finite groups with all ...
H. Smith, G. Cutolo
doaj  

Groups with all Subgroups Subnormal or Nilpotent-by-Chernikov

Rendiconti del Seminario Matematico della Università di Padova, 2011
An important result by \textit{W. Möhres} [Arch. Math. 54, No. 3, 232-235 (1990; Zbl 0663.20027)] shows that any group in which all subgroups are subnormal is soluble. Using this theorem, \textit{H. Smith} [Topics in infinite groups. Rome: Aracne. Quad. Mat.
openaire   +3 more sources

GROUPS WITH FINITELY MANY CONJUGACY CLASSES OF SUBGROUPS THAT ARE NOT NILPOTENT-BY-CHERNIKOV [PDF]

Glasgow Mathematical Journal, 2006
openaire   +1 more source

On nilpotent Chernikov p-groups with elementary tops

Archiv Der Mathematik, 2014
The description of nilpotent Chernikov $p$-groups with elementary tops is reduced to the study of tuples of skew-symmetric bilinear forms over the residue field $\mathbb{F}_p$.
Yuriy Drozd
exaly   +3 more sources

Groups in which every proper subgroup is ?ernikov-by-nilpotent or nilpotent-by-?ernikov

Archiv der Mathematik, 1988
\textit{B. Bruno} and \textit{R. E. Phillips} [Rend. Semin. Mat. Univ. Padova 69, 153-168 (1983; Zbl 0522.20022)] have classified infinite groups in which every proper subgroup is finite-by-nilpotent of class \(c\) whereas \textit{B. Bruno} [Boll. Unione Mat. Ital., VI. Ser. B 3, 797-807 (1984; Zbl 0563.20035) and ibid.
Otal, Javier, Peña, Juan Manuel
openaire   +1 more source

Locally Nilpotent p -Groups whose Proper Subgroups are Hypercentral or Nilpotent-by-Chernikov

Journal of the London Mathematical Society, 2000
A O Asar
exaly  

Groups with Chernikov factor-group by hypercentral

Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas, 2014
L A Kurdachenko, Javier Otal, Otal Javier   +2 more
exaly  

Locally finite groups containing a $$2$$ 2 -element with Chernikov centralizer

Monatshefte Fur Mathematik, 2014
E I Khukhro, N Yu Makarenko, Pavel Shumyatsky   +2 more
exaly  

Central-by-Chernikov groups are compact co-Chernikov CC-groups

Annali Di Matematica Pura Ed Applicata, 2003
Javier Otal
exaly