On the derived length of parasoluble groups

Alessio Russo

Bollettino dell'Unione Matematica Italiana (2003)

  • Volume: 6-B, Issue: 1, page 237-244
  • ISSN: 0392-4033

Abstract

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In this paper groups are considered inducing groups of power automorphisms on each factor of their derived series. In particular, it is proved that soluble groups with such property have derived length at most 3, and that this bound is best possible.

How to cite

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Russo, Alessio. "On the derived length of parasoluble groups." Bollettino dell'Unione Matematica Italiana 6-B.1 (2003): 237-244. <http://eudml.org/doc/195283>.

@article{Russo2003,
abstract = {In this paper groups are considered inducing groups of power automorphisms on each factor of their derived series. In particular, it is proved that soluble groups with such property have derived length at most 3, and that this bound is best possible.},
author = {Russo, Alessio},
journal = {Bollettino dell'Unione Matematica Italiana},
keywords = {groups of power automorphisms; derived series; strongly parasoluble groups; derived lengths},
language = {eng},
month = {2},
number = {1},
pages = {237-244},
publisher = {Unione Matematica Italiana},
title = {On the derived length of parasoluble groups},
url = {http://eudml.org/doc/195283},
volume = {6-B},
year = {2003},
}

TY - JOUR
AU - Russo, Alessio
TI - On the derived length of parasoluble groups
JO - Bollettino dell'Unione Matematica Italiana
DA - 2003/2//
PB - Unione Matematica Italiana
VL - 6-B
IS - 1
SP - 237
EP - 244
AB - In this paper groups are considered inducing groups of power automorphisms on each factor of their derived series. In particular, it is proved that soluble groups with such property have derived length at most 3, and that this bound is best possible.
LA - eng
KW - groups of power automorphisms; derived series; strongly parasoluble groups; derived lengths
UR - http://eudml.org/doc/195283
ER -

References

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  1. COOPER, C. D. H., Power automorphisms of a group, Math. Z., 107 (1968), 335-356. Zbl0169.33801MR236253
  2. FRANCIOSI, S.- DE GIOVANNI, F., Groups with many supersoluble subgroups, Ricerche Mat., 40 (1991), 321-333. Zbl0818.20041MR1194163
  3. ROBINSON, D. J. S., Groups in which normality is a transitive relation, Proc. Cambridge Philos. Soc., 60 (1964), 21-38. Zbl0123.24901MR159885
  4. ROBINSON, D. J. S., Finiteness Conditions and Generalized Soluble Groups, Springer, Berlin (1972). Zbl0243.20033
  5. WEHRFRITZ, B. A. F., Infinite Linear Groups, Springer, Berlin (1973). Zbl0261.20038MR335656
  6. WEIDIG, I., Gruppen mit abgeschwächter Normalteilertransitivität, Rend. Sem. Mat. Univ. Padova, 36 (1966), 185-215. Zbl0136.28301MR202845

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