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A self-centralizing characteristic subgroup

Published online by Cambridge University Press:  09 April 2009

M. D. Perez-Ramos
Affiliation:
Departamento de Algebra, Universidad de Valencia, C/Doctor Moliner, 50 46100 Burjassot Valencia, Spain
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Abstract

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

Type
Research Article
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), 118119.CrossRefGoogle Scholar
[2]Arad, Z., ‘Abelian and nilpotent subgroups of maximal order of groups of odd order’, Pacific J. Math. 62 (1976), 2935.CrossRefGoogle Scholar
[3]Arad, Z. and Chillag, D., ‘Injectors of finite solvable groups’, Comm. Algebra 7 (1979), 115138.CrossRefGoogle Scholar
[4]Bialostocki, A., ‘On products of two nilpotent subgroups of a finite group’, Israel J. Math. 20 (1975), 178188.CrossRefGoogle Scholar
[5]Blessenohl, D. and Laue, H., ‘Fittingklassen endlicher Gruppen, in denen gewise Hauptfaktoren einfach sind’, J. Algebra 56 (1979), 516532.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), 395399.CrossRefGoogle Scholar
[8]Glauberman, G., ‘A characteristic subgroup of a p-stable group’, Canad. J. Math. 20 (1968), 11011135.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), 123128.CrossRefGoogle Scholar
[12]Mann, A., ‘Injectors and normal subgroups of finite groups’, Israel J. Math. 9 (1971), 554558.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), 5159.CrossRefGoogle Scholar
[15]Perez-Ramos, M. D., ‘Stability with respect to a Fitting class’, J. Algebra, to appear.Google Scholar