On automorphisms fixing subnormal subgroups of soluble groups

Silvana Franciosi; Francesco de Giovanni

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1988)

  • Volume: 82, Issue: 2, page 217-222
  • ISSN: 0392-7881

Abstract

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The group A ⁢ u ⁢ t s ⁢ n ⁢ G of all automorphisms leaving invariant every subnormal subgroup of the group G is studied. In particular it is proved that A ⁢ u ⁢ t s ⁢ n ⁢ G is metabelian if G is soluble, and that A ⁢ u ⁢ t s ⁢ n ⁢ G is either finite or abelian if G is polycyclic.

How to cite

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Franciosi, Silvana, and de Giovanni, Francesco. "On automorphisms fixing subnormal subgroups of soluble groups." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 82.2 (1988): 217-222. <http://eudml.org/doc/289078>.

@article{Franciosi1988,
abstract = {The group $Aut_\{sn\} G$ of all automorphisms leaving invariant every subnormal subgroup of the group $G$ is studied. In particular it is proved that $Aut_\{sn\} G$ is metabelian if $G$ is soluble, and that $Aut_\{sn\} G$ is either finite or abelian if $G$ is polycyclic.},
author = {Franciosi, Silvana, de Giovanni, Francesco},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
keywords = {Automorphisms; Subnormal subgroups; Soluble groups},
language = {eng},
month = {6},
number = {2},
pages = {217-222},
publisher = {Accademia Nazionale dei Lincei},
title = {On automorphisms fixing subnormal subgroups of soluble groups},
url = {http://eudml.org/doc/289078},
volume = {82},
year = {1988},
}

TY - JOUR
AU - Franciosi, Silvana
AU - de Giovanni, Francesco
TI - On automorphisms fixing subnormal subgroups of soluble groups
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1988/6//
PB - Accademia Nazionale dei Lincei
VL - 82
IS - 2
SP - 217
EP - 222
AB - The group $Aut_{sn} G$ of all automorphisms leaving invariant every subnormal subgroup of the group $G$ is studied. In particular it is proved that $Aut_{sn} G$ is metabelian if $G$ is soluble, and that $Aut_{sn} G$ is either finite or abelian if $G$ is polycyclic.
LA - eng
KW - Automorphisms; Subnormal subgroups; Soluble groups
UR - http://eudml.org/doc/289078
ER -

References

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  1. COOPER, C.D.H., Power automorphisms of a group, «Math. Z.» 707 (1968), 335-356. Zbl0169.33801MR236253
  2. S. FRANCIOSI and DE GIOVANNI, F., On automorphisms fixing normal subgroups of nilpotent groups, «Boll. Un. Mat. Ital.», (7) 1 B (1987), 1161-1170. Zbl0635.20014MR923446
  3. GASCHÜTZ, W., Gruppen in denen das Normalteilersein transitiv ist, «J. Reine Angew. Math.» 198 (1957), 87-92. Zbl0077.25003MR91277
  4. HALL, P., Some sufficient conditions for a group to be nilpotent, «Illinois J. Math.» 2 (1958), 787-801. Zbl0084.25602MR105441
  5. LEINEN, F., Existenziell abgeschlossene LX-Gruppen, «Dissertation (Albert-Ludwigs Universität Freiburg i. Br.)», 1984. Zbl1098.20503
  6. ROBINSON, D.J.S., Groups in which normality is a transitive relation, «Proc. Cambridge Philos. Soc.» 60 (1964), 21-38. Zbl0123.24901MR159885
  7. ROBINSON, D.J.S., On finitely generated soluble groups, «Proc. London Math. Soc.» (3) 15 (1965), 508-516. Zbl0132.26801MR175977
  8. ROBINSON, D.J.S., Finiteness Conditions and Generalized Soluble Groups, Springer, Berlin, 1972. Zbl0243.20033

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