On maximal subgroups of minimax groups

Silvana Franciosi; Francesco de Giovanni

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1995)

  • Volume: 6, Issue: 1, page 23-27
  • ISSN: 1120-6330

Abstract

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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.

How to cite

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Franciosi, Silvana, and de Giovanni, Francesco. "On maximal subgroups of minimax groups." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 6.1 (1995): 23-27. <http://eudml.org/doc/244086>.

@article{Franciosi1995,
abstract = {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.},
author = {Franciosi, Silvana, de Giovanni, Francesco},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Minimax group; Frattini subgroup; Finite-by-nilpotent group; finitely generated soluble groups; soluble residually finite minimax groups; finite-by-nilpotent groups; maximal subgroups},
language = {eng},
month = {3},
number = {1},
pages = {23-27},
publisher = {Accademia Nazionale dei Lincei},
title = {On maximal subgroups of minimax groups},
url = {http://eudml.org/doc/244086},
volume = {6},
year = {1995},
}

TY - JOUR
AU - Franciosi, Silvana
AU - de Giovanni, Francesco
TI - On maximal subgroups of minimax groups
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1995/3//
PB - Accademia Nazionale dei Lincei
VL - 6
IS - 1
SP - 23
EP - 27
AB - 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.
LA - eng
KW - Minimax group; Frattini subgroup; Finite-by-nilpotent group; finitely generated soluble groups; soluble residually finite minimax groups; finite-by-nilpotent groups; maximal subgroups
UR - http://eudml.org/doc/244086
ER -

References

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  1. LENNOX, J. C., Finite Frattini factors in finitely generated soluble groups. Proc. Amer. Math. Soc., 41, 1973, 356-360. Zbl0277.20045MR333003
  2. LENNOX, J. C., Finite by nilpotent Frattini factors in finitely generated hyper(abelian by finite) groups. Arch. Math. (Basel), 25, 1974, 463-465. Zbl0295.20034MR404459
  3. ROBINSON, D. J. S., Residual properties of some classes of infinite soluble groups. Proc. London Math. Soc., (3), 18, 1968, 495-520. Zbl0157.05402MR228586
  4. ROBINSON, D. J. S., A theorem on finitely generated hyperabelian groups. Invent. Math., 10, 1970, 38-43. Zbl0198.34504MR265450
  5. ROBINSON, D. J. S., Finiteness Conditions and Generalized Soluble Groups. Springer, Berlin1972. Zbl0243.20033
  6. ROBINSON, D. J. S., The vanishing of certain homology and cohomology groups. J. Pure Appl. Algebra, 7, 1976, 145-167. Zbl0329.20032MR404478
  7. ROBINSON, D. J. S., A Course in the Theory of Groups. Springer, Berlin1982. Zbl0836.20001MR648604
  8. WEHRFRITZ, B. A. F., Infinite Linear Groups. Springer, Berlin1973. Zbl0261.20038MR335656

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