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CLT groups and wreath products

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

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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

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