Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-24T22:44:39.239Z Has data issue: false hasContentIssue false
  • English
  • Français

CLT groups and wreath products

Part of: Structure and classification of infinite or finite groups Representation theory of groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Rolf Brandl
Rolf Brandl
Affiliation:
Mathematisches InstitutAm Hubland 12 D-8700 Würzburg Federal Republic of, Germany
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 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.

MSC classification

Secondary: 20C05: Group rings of finite groups and their modules 20D60: Arithmetic and combinatorial problems 20E22: Extensions, wreath products, and other compositions 20F16: Solvable groups, supersolvable groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 42 , Issue 2 , April 1987 , pp. 183 - 195
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Bray, H. G., ‘A note on CLT groups’, Pacific J. Math. 27 (1968), 229–231.CrossRefGoogle Scholar
[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. 51–52).CrossRefGoogle Scholar
[3]Gow, R., ‘Groups whose characters are rational-valued’, J. Algebra 40 (1976), 280–299.CrossRefGoogle Scholar
[4]Humphreys, J. F. and Johnson, D. L., ‘On Lagrangian groups’, Trans. Amer. Math. Soc. 180 (1973), 291–300.CrossRefGoogle Scholar
[5]Huppert, B., Endliche Gruppen I (Springer-Verlag, Berlin and New York, 1967).CrossRefGoogle Scholar
[6]Huppert, B. and Blackburn, N., Finite Groups II (Springer-Verlag, Berlin and New York, 1982).CrossRefGoogle Scholar
[7]Kindermann, D., ‘Kranzprodukte und ein Satz von Lagrange’, Zulassungsarbeit Würzburg (1979).Google Scholar
[8]Michler, G. O., ‘Blocks and centers of group algebras’, (Lecture Notes in Mathematics, Vol. 246, Springer-Verlag, Berlin and New York, 1972, pp. 430–552).CrossRefGoogle Scholar
[9]Neumann, P. M., ‘On the structure of standard wreath products of groups’, Math. Z. 84 (1964), 343–373.CrossRefGoogle Scholar