Baer-elation planes (Q1098093)

The authors classify translation planes of even order q 2 and kernel GF(q) that admit an elation group of order q and a non-trivial Baer group or a Baer group of order q and a non-trivial elation group. Translation planes of the second sort with elations with at least two axes in the translation complement turn out to be the translation planes of Hall. The results are based, among others, on earlier papers of the two authors [see J. Lond. Math. Soc., II. Ser. 32, 297-304 (1985; Zbl 0586.51009) and Eur. J. Comb. 7, 227-235 (1986; Zbl 0612.51002)].