## Abstract

Let K be an extension of the field Q_{p} of p-adic rationals, let O_{K} be its ring of integers, and let G be a finite group. According to the classical Jordan–Zassenhaus Theorem, if K∕Q_{p} is finite, every isomorphism class of KG-representation modules splits in a finite number of isomorphism classes of O_{K}G-representation modules. We consider a p-group G of a given nilpotency class k>1 and the extension K∕Q_{p} where K=Q_{p}(ζ_{p∞ }) obtained by adjoining all roots ζ_{pi },i=1,2,3,. of unity, and we use an explicit combinatorial construction of a faithful absolutely irreducible KG-module M to show that the number of O_{K}G-isomorphism classes of O_{K}G-representation modules, which are KG-equivalent to M, is infinite, and there are extra congruence properties for these O_{K}G-modules.

Original language | English |
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Pages (from-to) | 287-295 |

Number of pages | 9 |

Journal | European Journal of Combinatorics |

Volume | 80 |

DOIs | |

Publication status | Published - Aug 2019 |

Externally published | Yes |

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics