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11.22 (1990)

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Characterize all $p$-groups, $p$ a prime, that can be faithfully represented as $n \times n$ triangular matrices over a division ring of characteristic $p$.

Contributor: B. A. F. Wehrfritz

Progress

If $p \geqslant n$ the solution is given in (B. A. F. Wehrfritz, Bull. London Math. Soc., 19 (1987), 320–324). The corresponding question with $p = 0$ was solved by B. Hartley and P. Menal (Bull. London Math. Soc., 15 (1983), 378–383), but see above reference for a second proof.

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