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Subgroups of Twisted Wreath Products

Published online by Cambridge University Press:  15 April 2019

By
Péter P. Pálfy
Edited by
C. M. Campbell ,
C. W. Parker ,
M. R. Quick ,
E. F. Robertson  and
C. M. Roney-Dougal
C. M. Campbell
Affiliation:
University of St Andrews, Scotland
C. W. Parker
Affiliation:
University of Birmingham
M. R. Quick
Affiliation:
University of St Andrews, Scotland
E. F. Robertson
Affiliation:
University of St Andrews, Scotland
C. M. Roney-Dougal
Affiliation:
University of St Andrews, Scotland
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Summary

By determining subdirect products invariant under the action of a regular permutation group of the components we provide a natural motivation for the definition of twisted wreath products. Then—based on papers of R. Baddeley, A. Lucchini, F. Börner, and M. Aschbacher—we explain how twisted wreath products play a fundamental role in the problem of representing finite lattices as intervals in subgroup lattices of finite groups.

Type
Chapter
Information
Groups St Andrews 2017 in Birmingham , pp. 455 - 468
Publisher: Cambridge University Press
Print publication year: 2019

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