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On finite products of totally permutable groups

Published online by Cambridge University Press:  17 April 2009

A. Ballester-Bolinches ,
M.C. Pedraza-Aguilera  and
M.D. Pérez-Ramos
A. Ballester-Bolinches
Affiliation:
Departament d'AlgebraUniversitat de ValènciaC/- Doctor Moliner, 5046100 Burjassot (València)Spain
M.C. Pedraza-Aguilera
Affiliation:
Departament d'AlgebraUniversitat de ValènciaC/- Doctor Moliner, 5046100 Burjassot (València)Spain
M.D. Pérez-Ramos
Affiliation:
Departament d'AlgebraUniversitat de ValènciaC/- Doctor Moliner, 5046100 Burjassot (València)Spain
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Abstract

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In this paper the structure of finite groups which are the product of two totally permutable subgroups is studied. In fact we can obtain the -residual, where is a formation, -projectors and -normalisers, where is a saturated formation, of the group from the corresponding subgroups of the factor subgroups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 53 , Issue 3 , June 1996 , pp. 441 - 445
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Ballester-Bolinches, A. and Pérez-Ramos, M.D., ‘A Question of R. Maier concerning formations’, (preprint).Google Scholar
[2]Ballester-Bolinches, A. and Pérez-Ramos, M.D., ‘On -subnormal subgroups and Frattini-like subgroups of a finite group’, Glasgow Math. J. 36 (1994), 241–247.CrossRefGoogle Scholar
[3]Doerk, K. and Hawkes, T., Finite soluble groups (Walter De Gruyter, Berlin, New York, 1992).CrossRefGoogle Scholar
[4]Maier, R., ‘A completeness property of certain formations’, Bull. London. Math. Soc. 24 (1992), 540–544.CrossRefGoogle Scholar