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On E-groups in the sense of Peng

Published online by Cambridge University Press:  18 May 2009

Hermann Heineken
Hermann Heineken
Affiliation:
Universität Würzburg, Fed. Rep. Germany
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The groups G of the title are those in which EG(x) = {y | y ∈ G, [y, nx] = 1 for some n} is a subgroup for every x in G. We show that the quotient group G/F(G) is rather restricted for finite E-groups; in particular, soluble finite E-groups are of Fitting length 4 at most. Some criteria for infinite groups are given.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 31 , Issue 2 , May 1989 , pp. 231 - 242
Copyright
Copyright © Glasgow Mathematical Journal Trust 1989

References

1.Baer, R., Engelsche Elemente Noetherscher Gruppen, Math. Ann. 133 (1957), 256–270.CrossRefGoogle Scholar
2.Casolo, C., Finite groups in which subnormalizers are subgroups, to appear.Google Scholar
3.Gaschütz, W., Gruppen, in denen das Normalteilersein transitiv ist, J. Reine Angew. Math. 198 (1957), 87–92.CrossRefGoogle Scholar
4.Hall, P., Some sufficient conditions for group to be nilpotent, Illinois J. Math. 2 (1958), 787–801.CrossRefGoogle Scholar
5.Huppert, B., Endliche Gruppen I (Springer, 1967).CrossRefGoogle Scholar
6.Messingschlager, W., E-Gruppen im Sinne von Peng, Diplomarbeit (Würzburg, 1987).Google Scholar
7.Peng, T. A., Finite soluble groups with an Engel condition, J. Algebra 11 (1969), 319–330.CrossRefGoogle Scholar
8.Peng, T. A., On groups with nilpotent derived groups, Arch. Math. Basel 20 (1969) 251–253.CrossRefGoogle Scholar
9.Peng, T. A., Ph.D. Thesis (Queen Mary College, University of London, 1965).Google Scholar
10.Robinson, D. J. S., Groups in which normality is a transitive relation, Proc. Cambridge Philos. Soc. 60 (1964), 21–38.CrossRefGoogle Scholar
11.Zassenhaus, H., Über endliche Fastkörper, Abh. Math. Sem. Univ. Hamburg 11 (1936), 187–220.CrossRefGoogle Scholar