Cover-avoidance and Frattini argument

Brewster, Ben; Hauck, Peter

doi:10.1090/S0002-9939-1991-1062828-1

Cover-avoidance and Frattini argument

Authors: Ben Brewster and Peter Hauck
Journal: Proc. Amer. Math. Soc. 113 (1991), 625-632
MSC: Primary 20D10
DOI: https://doi.org/10.1090/S0002-9939-1991-1062828-1
MathSciNet review: 1062828
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The results presented here develop further aspects of the theory of Fitting functors in finite (solvable) groups. These ideas evolved in investigating whether a Fitting functor with the cover-avoidance property necessarily satisfies the Frattini argument. Our results might be seen as an indication for a positive answer.

[1] James C. Beidleman, Ben Brewster, and Peter Hauck, Fittingfunktoren in endlichen auflösbaren Gruppen. I, Math. Z. 182 (1983), no. 3, 359–384 (German). MR 696533, https://doi.org/10.1007/BF01179756
[2] James C. Beidleman, Ben Brewster, and Peter Hauck, Fitting functors in finite solvable groups. II, Math. Proc. Cambridge Philos. Soc. 101 (1987), no. 1, 37–55. MR 877699, https://doi.org/10.1017/S0305004100066391
[3] James C. Beidleman and M. Pilar Gállego, Conjugate 𝜋-normally embedded Fitting functors, Rend. Sem. Mat. Univ. Padova 80 (1988), 65–82 (1989). MR 988113
[4] James C. Beidleman and Peter Hauck, Closure properties for Fitting functors, Monatsh. Math. 108 (1989), no. 1, 1–22. MR 1018821, https://doi.org/10.1007/BF01300063
[5] Dieter Blessenohl and Wolfgang Gaschütz, Über normale Schunck- und Fittingklassen, Math. Z. 118 (1970), 1–8 (German). MR 0277611, https://doi.org/10.1007/BF01109888
[6] M. P. Gállego, Fitting functors and normal products, Rev. Acad. Cienc. Zaragoza (2) 40 (1985), 9–12 (Spanish, with English summary). MR 850227
[7] M. Pilar Gállego, The radical of the Fitting class defined by a Fitting functor and a set of primes, Arch. Math. (Basel) 48 (1987), no. 1, 36–39. MR 878005, https://doi.org/10.1007/BF01196352
[8] Peter Hauck and Reinhold Kienzle, Modular Fitting functors in finite groups, Bull. Austral. Math. Soc. 36 (1987), no. 3, 475–483. MR 923830, https://doi.org/10.1017/S0004972700003774
[9] Trevor Hawkes, Subgroup embedding properties, Group theory (Bressanone, 1986) Lecture Notes in Math., vol. 1281, Springer, Berlin, 1987, pp. 52–64. MR 921690, https://doi.org/10.1007/BFb0078690
[10] F. Peter Lockett, The Fitting class 𝔉, Math. Z. 137 (1974), 131–136. MR 0364435, https://doi.org/10.1007/BF01214854