Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-24T06:34:06.679Z Has data issue: false hasContentIssue false
  • English
  • Français

Fitting classes and lattice formations I

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

M. Arroyo-Jordá  and
M. D. Pérez-Ramos
M. Arroyo-Jordá
Affiliation:
Departamento de Matemática AplicadaUniversidad Politécnica de ValenciaCamino de Vera, s/n46071 Valencia, Spain, e-mail: marroyo @mat.upv.es
M. D. Pérez-Ramos
Affiliation:
Departamento d'ÀlgebraUniversitat de València, Doctor Moliner 5046100 Burjassot (València), Spain, e-mail: [email protected]
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.

A lattice formation is a class of groups whose elements are the direct product of Hall subgroups corresponding to pairwise disjoint sets of primes. In this paper Fitting classes with stronger closure properties involving F-subnormal subgroups, for a lattice formation F of full characteristic, are studied. For a subgroup-closed saturated formation G, a characterisation of the G-projectors of finite soluble groups is also obtained. It is inspired by the characterisation of the Carter subgroups as the N-projectors, N being the class of nilpotent groups.

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 76 , Issue 1 , February 2004 , pp. 93 - 108
Copyright
Copyright © Australian Mathematical Society 2004

References

REFERENCES

[1]Arroyo-Jord´, M., F-Normalidad (Ph.D. Thesis, Universitat de València, 2000).Google Scholar
[2]Arroyo-Jord´, M. and Pérez-Ramos, M. D., ‘Fitting classes and lattice formations II’, J. Aust. Math. Soc., to appear.Google Scholar
[3]Arroyo-Jord´, M. and Pérez-Ramos, M. D., ‘On the lattice of F-Dnormal subgroups in finite soluble groups’, J. Algebra 242 (2001), 198–212.CrossRefGoogle Scholar
[4]Ballester-Bolinches, A., ‘A note on saturated formations’, Arch. Math. 58 (1992), 110–113.CrossRefGoogle Scholar
[5]Ballester-Bolinches, A., Doerk, K. and Pérez-Ramos, M. D., ‘On the lattice of F-subnormal subgroups’, J. Algebra 148 (1992), 42–52.CrossRefGoogle Scholar
[6]Ballester-Bolinches, A., Doerk, K. and Pérez-Ramos, M. D., ‘On F-normal subgroups of finite soluble groups’, J. Algebra 171 (1995), 189–203.CrossRefGoogle Scholar
[7]Ballester-Bolinches, A., Martínez-Pastor, A. and Pérez-Ramos, M. D., ‘Nilpotent-like Fitting formations of finite soluble groups’, Bull. Austral. Math. Soc. 62 (2000), 427–433.CrossRefGoogle Scholar
[8]Ballester-Bolinches, A., Pedraza-Aguilera, M. C. and Pérez-Ramos, M. D., ‘On F-subnormal subgroups and F-residuals of finite soluble groups’, J. Algebra 186 (1996), 314–322.CrossRefGoogle Scholar
[9]Ballester-Bolinches, A. and Pérez-Ramos, M. D., ‘On F-critical groups’, J. Algebra 174 (1995), 948–958.CrossRefGoogle Scholar
[10]Ballester-Bolinches, A. and Pérez-Ramos, M. D., ‘Two questions of L. A. Shemetkov on critical groups’, J. Algebra 179 (1996), 905–917.CrossRefGoogle Scholar
[11]Carter, R. and Hawkes, T., ‘The F-normalizers of a finite soluble group’, J. Algebra 5 (1967), 175–202.CrossRefGoogle Scholar
[12]Doerk, K. and Hawkes, T., Finite soluble groups (Walter De Gruyter, Berlin, 1992).CrossRefGoogle Scholar
[13]Förster, P., ‘Finite groups all of whose subgroups are F-subnormal or F-subabnormal’, J. Algebra 103 (1986), 285–293.CrossRefGoogle Scholar
[14]Graddon, C. J., ‘F-reducers in finite soluble groups’, J. Algebra 18 (1971), 574–587.CrossRefGoogle Scholar
[15]Lockett, F. P., On the theory of Fitting classes of fintte soluble groups (Ph.D. Thesis, University of Warwick, 1971).Google Scholar
[16]Müller, N., ‘F-Pronormale Untergruppen Endlich Auflösbarer Gruppen’, preprint, 1985.Google Scholar