8.1 (1982)

Open

Characterize all groups (or at least all soluble groups) $G$ and fields $F$ such that every irreducible $FG$-module has finite dimension over the centre of its endomorphism ring.

Progress

For some partial answers see (B. A. F. Wehrfritz, Glasgow Math. J., 24, no. 1 (1983), 169–176).

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