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CLT groups and wreath products

  • Rolf Brandl (a1)

Abstract

In this paper the question is considered of when the wreath product of a nilpotent group with a CLT group G is a CLT group. It is shown that if the field with Pr elements is a splitting field of a Hall P1–subgroup of G, then P wr G is a CLT group for all p–groups P with |P/P1|≥ pr. Moreover, the class of all groups G having the property that N wr G is a CLT group for every nilpotent group N is shown to be quite large. For exmple, every group of odd order can be embedded as a subgroup of a group belonging to this class.

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References

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[1]Bray, H. G., ‘A note on CLT groups’, Pacific J. Math. 27 (1968), 229231.
[2]Gagen, T., ‘A note on groups with the inverse Lagrange property’ (Group Theory, Canberra, 1975. Lecture Notes in Mathematics, Vol. 573, Springer-Verlag, Berlin and New York, 1977, pp. 5152).
[3]Gow, R., ‘Groups whose characters are rational-valued’, J. Algebra 40 (1976), 280299.
[4]Humphreys, J. F. and Johnson, D. L., ‘On Lagrangian groups’, Trans. Amer. Math. Soc. 180 (1973), 291300.
[5]Huppert, B., Endliche Gruppen I (Springer-Verlag, Berlin and New York, 1967).
[6]Huppert, B. and Blackburn, N., Finite Groups II (Springer-Verlag, Berlin and New York, 1982).
[7]Kindermann, D., ‘Kranzprodukte und ein Satz von Lagrange’, Zulassungsarbeit Würzburg (1979).
[8]Michler, G. O., ‘Blocks and centers of group algebras’, (Lecture Notes in Mathematics, Vol. 246, Springer-Verlag, Berlin and New York, 1972, pp. 430552).
[9]Neumann, P. M., ‘On the structure of standard wreath products of groups’, Math. Z. 84 (1964), 343373.
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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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