Unitary units in modular group algebras

Victor Bovdi, L. G. Kovács

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)

Abstract

Let p be a prime, K a field of characteristic p, G a locally finite p-group, KG the group algebra, and V the group of the units of KG with augmentation 1. The anti-automorphism g→g -1 of G extends linearly to KG; this extension leaves V setwise invariant, and its restriction to V followed by v→v -1 gives an automorphism of V. The elements of V fixed by this automorphism are called unitary; they form a subgroup. Our first theorem describes the K and G for which this subgroup is normal in V. For each element g in G, let {Mathematical expression} denote the sum (in KG) of the distinct powers of g. The elements 1+(g-1) {Mathematical expression} with h,hεG are the bicyclic units of KG. Our second theorem describes the K and G for which all bicyclic units are unitary.

Original languageEnglish
Pages (from-to)57-72
Number of pages16
JournalManuscripta Mathematica
Volume84
Issue number1
DOIs
Publication statusPublished - Dec 1994
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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