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Let be a finite field of characteristic and a field which contains a primitive th root of unity and . Suppose that a classical group acts on the -vector space . Then it can induce the actions on the vector space and on the group algebra , respectively. In this paper we determine the structure of -invariant ideals of the group algebra , and establish the relationship between the invariant ideals of and the vector invariant ideals of , if is a unitary group or orthogonal group....
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