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2 results

  • An Induction Theorem for Units of p-Adic Group Rings

  • A. K. Bhandari, S. K. Sehgal
  • Journal:
    Canadian Mathematical Bulletin / Volume 34 / Issue 1 / 01 March 1991
    Published online by Cambridge University Press:
    20 November 2018, pp. 31-35
    Print publication:
    01 March 1991
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  • Let G be a finite group and let C be the family of cyclic subgroups of G. We show that the normal subgroup H of U = U(ZpG) generated by U(ZpC), C ∊ C, where Zp is the ring of p-adic integers, is of finite index in U.

  • Généralisation d'un Lemme de Kummer*

  • Klaus Hoechsmann
  • Journal:
    Canadian Mathematical Bulletin / Volume 32 / Issue 4 / 01 December 1989
    Published online by Cambridge University Press:
    20 November 2018, pp. 486-489
    Print publication:
    01 December 1989
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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.