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SCHREIER CONDITIONS ON CHIEF FACTORS AND RESIDUALS OF SOLVABLE-LIKE GROUP FORMATIONS

Part of: Structure and classification of infinite or finite groups Representation theory of groups

Published online by Cambridge University Press:  01 August 2008

GIL KAPLAN  and
DAN LEVY
GIL KAPLAN
Affiliation:
The School of Computer Sciences, The Academic College of Tel-Aviv-Yaffo, 4 Antokolsky St., Tel-Aviv 64044, Israel
DAN LEVY*
Affiliation:
The School of Computer Sciences, The Academic College of Tel-Aviv-Yaffo, 4 Antokolsky St., Tel-Aviv 64044, Israel (email: [email protected])
*
✉For correspondence.
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Abstract

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Let α be a formation of finite groups which is closed under subgroups and group extensions and which contains the formation of solvable groups. Let G be any finite group. We state and prove equivalences between conditions on chief factors of G and structural characterizations of the α-residual and theα-radical of G. We also discuss the connection of our results to the generalized Fitting subgroup of G.

Keywords

Schreier’s conjectureresidualradicalchief factorsgeneralized Fitting subgroup

MSC classification

Secondary: 20D25: Special subgroups (Frattini, Fitting, etc.) 20E34: General structure theorems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 78 , Issue 1 , August 2008 , pp. 97 - 106
Copyright
Copyright © 2008 Australian Mathematical Society

References

[1]Holt, D. F., Handbook of Computational Group Theory (Chapman & Hall/CRC Press, Boca Raton, FL, 2005).CrossRefGoogle Scholar
[2]Huppert, B. and Blackburn, N., Finite Groups (Springer, Berlin, 1982).Google Scholar
[3]Kurzweil, H. and Stellmacher, B., The Theory of Finite Groups, an Introduction (Springer, Berlin, 2004).CrossRefGoogle Scholar
[4]Robinson, D. J. S., ‘The structure of finite groups in which permutability is a transitive relation’, J. Austral. Math. Soc. 70 (2001), 143–149.CrossRefGoogle Scholar
[5]Rose, J. S., A Course on Group Theory (Dover Publications/Cambridge University Press, Cambridge, 1978).Google Scholar
[6]Seress, A., Permutation Group Algorithms, Cambridge Tracts in Mathematics, 152 (Cambridge University Press, Cambridge, 2003).CrossRefGoogle Scholar