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8.49 (1982)

Solved

Let $G$ be a $p$-group acting transitively as a permutation group on a set $\Omega$, let $F$ be a field of characteristic $p$, and regard $F\Omega$ as an $FG$-module. Then do the descending and ascending Loewy series of $F\Omega$ coincide?

Contributor: P. M. Neumann

Progress

Yes, they do (J. L. Alperin, Quart. J. Math. Oxford (2), 39, no. 154 (1988), 129–133).

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