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Généralisation d'un Lemme de Kummer*

Published online by Cambridge University Press:  20 November 2018

Klaus Hoechsmann
Klaus Hoechsmann*
Affiliation:
University of British Columbia Vancouver, Canada
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Abstract

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If A is a finite abelian group and ZA its integral group ring, consider units u ∊ ZA which have coefficient sum = 1 and are fixed under the involution a —> a-1, a ∊ A. For an odd regular prime p and a p-group A, it is shown that u ≡ 1 mod p if only if u = π(v)v-p, where v is the same kind of unit, and π is the ring endomorphism given by a —> ap, a∊A.

Keywords

20C0516A2516A18
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 4 , 01 December 1989 , pp. 486 - 489
Copyright
Copyright © Canadian Mathematical Society 1989

Footnotes

*

Travail subventionné par le CRSNG du Canada.

References

Bibliographie

1. Hasse, H., Zahlenîheorie, Akademie-Verlag, Berlin (1963).Google Scholar
2. Hoechsmann, K. and S. K. Sehgal, Units in regular abelian p-groups rings, J. of Number Theory 30, 375-381 (1988).Google Scholar
3. Hoechsmann, K. and J. Ritter, Logarithms and units in p-adic p-group rings, Arch. d. Math., 49, 23–28 (1987).Google Scholar
4. Kummer, E., Beweis des Fermât'schen Satzes der Unmöglichkeit von xλ+yλ = zλ fur eine unendliche Anzahl Primzahlen λ, Monatsber. Akad. Wiss. Berlin, 1847, 305-319; Collected Papers I, p. 297.Google Scholar