Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-27T23:19:42.187Z Has data issue: false hasContentIssue false
  • English
  • Français

A self-centralizing characteristic subgroup

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

M. D. Perez-Ramos
M. D. Perez-Ramos
Affiliation:
Departamento de Algebra, Universidad de Valencia, C/Doctor Moliner, 50 46100 Burjassot Valencia, Spain
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this note we introduce a self-centralizing characteristic subgroup, associated with quasinilpotent injectors, of a finite group.

MSC classification

Secondary: 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 46 , Issue 2 , April 1989 , pp. 302 - 307
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Arad, Z., ‘II'-closure of finite II-solvable groups’, J. Austral. Math. Soc. Ser. A. 21 (1976), 118–119.CrossRefGoogle Scholar
[2]Arad, Z., ‘Abelian and nilpotent subgroups of maximal order of groups of odd order’, Pacific J. Math. 62 (1976), 29–35.CrossRefGoogle Scholar
[3]Arad, Z. and Chillag, D., ‘Injectors of finite solvable groups’, Comm. Algebra 7 (1979), 115–138.CrossRefGoogle Scholar
[4]Bialostocki, A., ‘On products of two nilpotent subgroups of a finite group’, Israel J. Math. 20 (1975), 178–188.CrossRefGoogle Scholar
[5]Blessenohl, D. and Laue, H., ‘Fittingklassen endlicher Gruppen, in denen gewise Hauptfaktoren einfach sind’, J. Algebra 56 (1979), 516–532.CrossRefGoogle Scholar
[6]Ezquerro, L. M., ‘F-estabilidad, constriccion y factorizacion de grupos finitos’, Tesis Doctoral, U. de Valencia (1983).Google Scholar
[7]Ezquerro, L. M., ‘F-stability of finite groups’, J. Algebra 92 (1985), 395–399.CrossRefGoogle Scholar
[8]Glauberman, G., ‘A characteristic subgroup of a p-stable group’, Canad. J. Math. 20 (1968), 1101–1135.CrossRefGoogle Scholar
[9]Gorenstein, D., Finite groups (Harper & Row, New York, 1968).Google Scholar
[10]Huppert, B. and Blackburn, N., Finite groups, II, III (Springer-Verlag, Berlin, 1982).Google Scholar
[11]Iranzo, M. J. and Monasor, F. Perez, ‘Existence of N-injectors in a not central normal Fitting class’, Israel J. Math. 48 (1984), 123–128.CrossRefGoogle Scholar
[12]Mann, A., ‘Injectors and normal subgroups of finite groups’, Israel J. Math. 9 (1971), 554–558.CrossRefGoogle Scholar
[13]Monasor, F. Perez, ‘Grupos finitos separados respecto de una formacion de Fitting’, Rev. Acad. Ciencias de Zaragoza, Serie 2 28 (1973).Google Scholar
[14]Perez-Ramos, M. D., ‘A characteristic subgroup of N-stable groups’, Israel J. Math. 54 (1986), 51–59.CrossRefGoogle Scholar
[15]Perez-Ramos, M. D., ‘Stability with respect to a Fitting class’, J. Algebra, to appear.Google Scholar