On the fitting length of NC-groups

Geometriae Dedicata - Tập 40 - Trang 117-124 - 1991
Anna Luisa Gilotti1, Fletcher Gross2, Umberto Tiberio3
1Istituto di Matematica, Università di Salerno, Baronissi-Salerno, Italy
2Department of Mathematics, University of Utah, Salt Lake City, USA
3Dipartimento di Matematica Applicata “G. Sansone”, Firenze, Italy

Tóm tắt

In this paper NC-groups (i.e. finite groups G, in which for every Sylow p-subgroup P of G, N G(Z(P))=C G(Z(P)) are studied. Mainly the Authors give a way to construct solvable NC-groups with arbitrarely large fitting length and trivial center. Further some results about nonsolvable NC-groups are given.

Tài liệu tham khảo

Gilotti, A. and Tiberio, U., ‘On the NC-groups’, Ricerche di Matematica Vol. XXXIX (1990), 71–79. Hauck, P., Personal communication. Gross, F., ‘Automorphisms which centralize a Sylow p-subgroup’, J. Algebra 77 (1982), 202–233. Huppert, B., Endliche Gruppen I, Springer-Verlag, 1967. Huppert, B. and Blackburn, N., Finite Groups III, Springer-Verlag, 1982. Suzuki, M., Group Theory I, Springer-Verlag, 1982. Suzuki, M., Group Theory II, Springer-Verlag, 1986.