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Group structure and properties of block ideals of the group algebra

Published online by Cambridge University Press:  18 May 2009

Wolfgang Hamernik
Wolfgang Hamernik
Affiliation:
Mathematisches Institut der Universität, D 63 Glessen, Arndtstr. 2, W. Germany
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In this note relations between the structure of a finite group G and ringtheoretical properties of the group algebra FG over a field F with characteristic p > 0 are investigated. Denoting by J(R) the Jacobson radical and by Z(R) the centre of the ring R, our aim is to prove the following theorem generalizing results of Wallace [10] and Spiegel [9]:

Theorem. Let G be a finite group and let F be an arbitrary field of characteristic p > 0. Denoting by BL the principal block ideal of the group algebra FG the following statements are equivalent:

(i) J(B1) ≤ Z(B1)

(ii) J(B1)is commutative,

(iii) G is p-nilpotent with abelian Sylowp-subgroups.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 16 , Issue 1 , March 1975 , pp. 22 - 28
Copyright
Copyright © Glasgow Mathematical Journal Trust 1975

References

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