Hostname: page-component-76fb5796d-dfsvx Total loading time: 0 Render date: 2024-04-26T12:36:54.740Z Has data issue: false hasContentIssue false
  • English
  • Français

Nilpotent-by-Černikov CC-groups

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Javier Otal  and
Juan Manuel Peña
Javier Otal
Affiliation:
Departmento de Matemáticas Facultad de CienciasUniversidad de Zaragoza50009 Zaragoza, Spain
Juan Manuel Peña
Affiliation:
Department de Matemática Aplicada E.U.I.T.I.Universidad de Zaragoza50009 Zaragoza, Spain
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.

In this paper we study groups with Černikov conjugacy classes which are nilpotent-by-Černikov groups, giving full characterizations of them and applying the results obtained to some related areas.

MSC classification

Secondary: 20F24: FC-groups and their generalizations 20F18: Nilpotent groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 53 , Issue 1 , August 1992 , pp. 120 - 130
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Alcázar, J. and Otal, J., ‘Sylow subgroups of groups with Černikov conjugacy classes’, J. Algebra 110 (1987), 507–513.CrossRefGoogle Scholar
[2]González, M., Otal, J. and Peña, J. M., ‘CC-groups with periodic central factor’, Manuscripta Math. 69 (1990), 93–105.CrossRefGoogle Scholar
[3]Hall, P., ‘Finite-by-nilpotent groups’, Proc. Cambridge Philos. Soc. 52 (1956), 611–616.CrossRefGoogle Scholar
[4]Hall, P., The Edmonton notes on nilpotent groups (Queen Mary College Mathematics Notes, London, 1969).Google Scholar
[5]Otal, J. and Peña, J. M., ‘Minimal non-CC-groups’, Comm. Algebra 16 (1988), 1231–1242.CrossRefGoogle Scholar
[6]Otal, J. and Peña, J. M., ‘Groups in which every proper subgroup is Černikov-by-nilpotent or nilpotent-by-Černikov’, Arch. Math. 51 (1988), 193–197.CrossRefGoogle Scholar
[7]Otal, J. and Peña, J. M., ‘Locally nilpotent injectors of CC-groups’, Contribuciones Matemáticas en Homenaje al Profesor D. Antonio Plans, pp. 233–238 (Universidad de Zaragoza, 1990).Google Scholar
[8]Otal, J. and Peña, J. M., ‘Sylow Theory of CC-groups’, Rend. Sem. Mat. Univ. Padova 85 (1991), 105–118.Google Scholar
[9]Otal, J., Peña, J. M. and Tomkinson, M. J., ‘Locally inner automorphisms of CC-groups’, J. Algebra 141 (1991), 382–398.CrossRefGoogle Scholar
[10]Polovickii, Ya. D., ‘On locally extremal groups and groups with the π-minimal condition’, Soviet Math. Dokl. 2 (1961), 780–782.Google Scholar
[11]Polovickii, Ya. D., ‘Locally extremal and layer-extremal groups’, Mat. Sb. 58 (1962), 685–694.Google Scholar
[12]Polovickii, Ya. D., ‘Groups with extremal classes of conjugate elements’, Sibirsk. Mat. Ž 5 (1964), 891–895.Google Scholar
[13]Robinson, D. J. S., Finiteness conditions and generalized soluble groups (Springer-Verlag, Berlin, Heidelberg, New York, 1972).CrossRefGoogle Scholar
[14]Tomkinson, M. J., FC-groups (Pitman, Boston, London, Melbourne, 1984).Google Scholar