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A local approach to a class of locally finite groups

Published online by Cambridge University Press:  17 April 2009

A. Ballester-Bolinches  and
Tatiana Pedraza
A. Ballester-Bolinches
Affiliation:
Department d'Àlgebra, Universitat de València, Dr. Moliner 50, 46100 Burjassot, València, Spain e-mail: Adolfo. [email protected]
Tatiana Pedraza
Affiliation:
Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, Escuela Politécnica Superior de Alcoy, 3801 Alcoy, Alicante, Spain e-mail: [email protected]
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Abstract

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This paper is devoted to the study of a class of generalised P-nilpotent groups in the universe c of all radical locally finite groups satisfying min-q for every prime q. Some results of finite groups are extended and a characterisation of the injectors associated with this class is given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 68 , Issue 1 , August 2003 , pp. 45 - 56
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Ballester-Bolinches, A. and Camp-Mora, S., ‘A Gaschütz-Lubeseder type theorem in a class of locally finite groups’, J. Algebra 221 (1999), 562–569.CrossRefGoogle Scholar
[2]Ballester-Bolinches, A. and Camp-Mora, S., ‘A Bryce-Cossey type theorem in a class of locally finite groups’, Bull. Austral. Math. Soc. 63 (2001), 459–466.Google Scholar
[3]Ballester-Bolinches, A. and Pedraza, T., ‘On a class of generalized nilpotent groups’ J. Algebra 248 (2002), 219–229.CrossRefGoogle Scholar
[4]Ballester-Bolinches, A. and Pedraza, T., ‘The fitting subgroup and some injectors of radical locally finite groups with min-P for all P’, Comm. Algebra 31 (2003), 483–492.CrossRefGoogle Scholar
[5]Dixon, M.R., ‘Certain fitting classes of groups with min-P for all P’ Arch. Math. (Basel) 54 (1990), 521–532.Google Scholar
[6]Dixon, M.R., Sylow theory, formations and fitting classes in locally finite groups, Series in Algebra 2 (World Scientific, River Edge, N.J., 1994).CrossRefGoogle Scholar
[7]Doerk, K. and Hawkes, T. O., Finite soluble groups, de Gruyter Expositions in Mathematics 4 (Walter De Gruyter, Berlin, 1992).CrossRefGoogle Scholar
[8]Iranzo, M.J. and Torres, M., ‘The P*P-injectors of a finite group’ Rend. Sem. Mat. Univ. Padova 82 (1989), 233–237.Google Scholar
[9]Lafuente, J., ‘Chief factors of finite groups with order a multiple of P’, Comm. Algebra 16 (1988), 1563–1580.Google Scholar
[10]Robinson, D.J.S., A course in the theory of groups, Graduate Texts in Mathematics 80 (Springer-Verlag, New York, Berlin, 1982).CrossRefGoogle Scholar
[11]Robinson, D.J.S., Finiteness conditions and generalized soluble groups, Volumes 1 and 2 (Springer-Verlag, Berlin, 1972).CrossRefGoogle Scholar
[12]Tomkinson, M.J., ‘A frattini-like subgroup’, Math. Proc. Cambridge Philos. Soc. 77 (1975), 247–257.CrossRefGoogle Scholar
[13]Tomkinson, M.J., ‘Finiteness conditions and a frattini-like subgroup’, Rend. Circ. Mat. Palermo 23 (1990), 321–335.Google Scholar
[14]Tomkinson, M.J., ‘Schunck classes and projectors in a class of locally finite groups’, Proc. Edinburgh Math. Soc. 38 (1995), 511–522.CrossRefGoogle Scholar