by Hertweck, Martin; Nebe, Gabriele

For a finite group G, the group Outcent(Z

_p

G) of outer central automorphisms of Z

_p

G only depends on the Morita equivalence class of Z

_p

G, which allows reduction to a basic order for its calculation. If the group ring is strongly related to a graduated order, it is often possible to give an explicit description of the basic order. In this paper, we show that Outcent(B)=1 for a block B of Z

_p

G with cyclic defect group. We also prove that Outcent(B₀⁽³⁾(A
₆))= 1 for the principal block B₀⁽³⁾(A
₆) of Z
₃
A
₆; this allows us to verify a conjecture of Zassenhaus for the perfect group of order 1080.

DOI: 10.1023/B:ALGE.0000026826.81439.3f
Print publication date: 5/1/2004
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