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Nilpotent-by-Černikov CC-groups

  • Javier Otal (a1) and Juan Manuel Peña (a2)

Abstract

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.

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Copyright

References

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[1]Alcázar, J. and Otal, J., ‘Sylow subgroups of groups with Černikov conjugacy classes’, J. Algebra 110 (1987), 507513.
[2]González, M., Otal, J. and Peña, J. M., ‘CC-groups with periodic central factor’, Manuscripta Math. 69 (1990), 93105.
[3]Hall, P., ‘Finite-by-nilpotent groups’, Proc. Cambridge Philos. Soc. 52 (1956), 611616.
[4]Hall, P., The Edmonton notes on nilpotent groups (Queen Mary College Mathematics Notes, London, 1969).
[5]Otal, J. and Peña, J. M., ‘Minimal non-CC-groups’, Comm. Algebra 16 (1988), 12311242.
[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), 193197.
[7]Otal, J. and Peña, J. M., ‘Locally nilpotent injectors of CC-groups’, Contribuciones Matemáticas en Homenaje al Profesor D. Antonio Plans, pp. 233238 (Universidad de Zaragoza, 1990).
[8]Otal, J. and Peña, J. M., ‘Sylow Theory of CC-groups’, Rend. Sem. Mat. Univ. Padova 85 (1991), 105118.
[9]Otal, J., Peña, J. M. and Tomkinson, M. J., ‘Locally inner automorphisms of CC-groups’, J. Algebra 141 (1991), 382398.
[10]Polovickii, Ya. D., ‘On locally extremal groups and groups with the π-minimal condition’, Soviet Math. Dokl. 2 (1961), 780782.
[11]Polovickii, Ya. D., ‘Locally extremal and layer-extremal groups’, Mat. Sb. 58 (1962), 685694.
[12]Polovickii, Ya. D., ‘Groups with extremal classes of conjugate elements’, Sibirsk. Mat. Ž 5 (1964), 891895.
[13]Robinson, D. J. S., Finiteness conditions and generalized soluble groups (Springer-Verlag, Berlin, Heidelberg, New York, 1972).
[14]Tomkinson, M. J., FC-groups (Pitman, Boston, London, Melbourne, 1984).
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