A Characterization of Permutation Modules Extending a Theorem of Weiss

  • John William MacQuarrie

    Departamento de Matemática, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil
  • Pavel Zalesskii

    Universidade de Brasília, Brazil
A Characterization of Permutation Modules Extending a Theorem of Weiss cover
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Abstract

Let GG be a finite pp-group with normal subgroup NN. A celebrated theorem of A. Weiss gives a sufficient condition for a ZpG\mathbb{Z}_pG-lattice to be a permutation module, looking only at its restriction to NN and its NN-fixed points. In case NN has order pp, we extend the condition of Weiss to a characterization.

Cite this article

John William MacQuarrie, Pavel Zalesskii, A Characterization of Permutation Modules Extending a Theorem of Weiss. Doc. Math. 25 (2020), pp. 1159–1169

DOI 10.4171/DM/772